The assist feature in depth

I can almost guarantee it's because you have ko'd allies and you just started fighting a bot right after a transformation/entrance cutscene. It means you are being "assist"ed by the ally, it's an actively induced stat increase.
In this image Krillin is awaiting revival in PQ 1, that faint blue visual effect is coming from him.
As soon as you enter the stage, Krillin is boosting your speed as you get to him.

Should you ever find yourself defeated and that circle pops up around your unconscious body, one of the options in your action window will be "assist". Lock on to any ally who is still mobile and hold down that command, the assist is active for as long as you hold the input.
The other actions in that window: "view next/view previous/view self" do not allow assist though, it must be through lock on.

You can assist allies without being in a KO'd state yourself if you use Emporers Sign or Hero's Flute. these moves keep you stationary but protected. ES is 10 seconds long and HF is 6 seconds long. Effects will apply to all allies and not just 1.

assist buffs are color coded and the effects go as follows[lists]

• All damage boosted -red ~10% increase to all damage per assist
  
  
• Ki generation - yellow ~about 19 ki per second per assist, just 1 outpaces the drain rate of Super Saiyan Blue Evolution
  
  
• Stamina generation - green ~about 28 stamina per second per assist, just 1 evens out with Kaioken x20 and outpaces Become Giant
  
  
• Health recovery - light blue ~very slow, the lowest grade of regen capsules are more effective
  
  
• Speed boost - navy blue ~roughly 25% from 1 assist allowing for more advanced combos, the distance of dodges increases too
  
  
• ??? - orange ~you're on your own for this one

• Saiyans- boost damage
  
  
• Earthlings- ki generation
  
  
• Majins- stamina generation
  
  
• Namekians- healing
  
  
• "Frieza" race- boost speed

/ Orange auras are an alternative buff and only come from specific cast characters. It's possible that they don't do anything or are broken. Maybe Xenoverse 1 has it right?

Every resource assist is treated like auto-recovery/auto-regain, so even your stamina from a green assist would be recovering at all times like with the Purification Awoken Skill. Just one green aura is enough to make you less punishable.

Let's say I got you interested. You know what does what and now you are wanting to figure out who does it. This list can clear all that up for you. Give a whole new layer to offline PQ team selection

Goku- ki

Krillin- speed

SSGSS Goku- ki

Kid Gohan- damage

Great Saiyaman- damage

Piccolo- health

Yamcha- damage

Raditz- damage

Prince of Destruction Vegeta- ki

Guldo- health

Jeice- damage

Turles- damage

Zarbon- damage

Frieza(1st form)- speed

Golden Frieza- damage

Cooler(Final Form)- damage

Android 16- damage

Android 18- damage

Cell(Full Power)- ki

Hercule- stamina

Majin Buu- stamina

Supervillain Kid Buu- damage

Broly- damage

Vegito- ki

Beerus- damage

Nuova Shenron- damage

Supervillain Omega Shenron- ki

Bardock- damage

Mira- damage

Trunks(Future)- health

SSG Goku- health

GT Goku- ki

Teen Gohan- damage

Future Gohan- damage

Supervillain Yamcha- damage

Nappa- stamina

SSGSS Vegeta- orange

Dodoria- damage

Recoome- stamina

Captain Ginyu- orange

Captain Ginyu (Vegeta's body) - ki

Captain Ginyu (Trunks' body) - stamina

Captain Ginyu (Goku's body) - orange

Lord Slug- damage

Frieza(FInal Form)- speed

Supervillain Golden Frieza- damage

Metal Cooler- damage

Android 17- speed

Cell(First Form)- damage

Supervillain Cell(Full Power)- damage

Videl- speed

Super Buu- damage

Janemba- damage

Supervillain Broly- damage

Gogeta(Super Saiyan)- damage

Whis- orange

Eis Shenron- speed

Pan- speed

Masked Saiyan- damage

Supervillain Mira- damage

GT Trunks- stamina

Kid Trunks- damage

SSJ4 Goku- ki

Adult Gohan- damage

Goten- speed

Tien- orange

Saibaman- damage

Kaiwareman- stamina

Kyukonman- orange

Copyman-health

Tennenman-speed

Jinkouman- ki

Vegeta- damage

SSJ4 Vegeta- ki

Nail- damage

Burter- speed

Appule- damage

Nabana- stamina

Roberry- orange

Ramon- health

Orlen- ki

Raspberry- stamina

Navel- orange

Monrei- damage

Guprei- ki

Frieza(Full Power)- speed

Cooler(Fourth Form)- damage

Supervillain Metal Cooler- damage

Super 17- orange

Perfect Cell- ki

Cell jr- speed

Great Saiyaman 2- speed

Kid Buu- ki

Supervillain Janemba- damage

Gotenks- ki

SSJ4 Gogeta- ki

Jaco- ki

Omega Shenron- ki

Hit- stamina

Towa- health

Goku Black- orange

Champa- damage

Rosé Goku Black- ki

SSGSS Vegito- damage

Android 13- ki

Jiren- damage

SSJ2 Kefla- damage

Broly(Full Power SSJ)- damage

SSG Vegeta- damage

Supreme Kai of Time- stamina

Jiren(Full Power)- damage

SSJ2 Kale- damage

GT Vegeta- orange

Gohan(Super Hero)- health

Orange Piccolo- damage

Zamasu- health

Super Buu(Gohan Absorbed)- health

Tapion- stamina

MUI Goku- ki

Super Baby 2- damage

Ribrianne- orange

Majuub- orange

Pikkon- health

Gogeta(DB Super)- damage

UI sign Goku- health

Gamma 1- damage

Gohan Beast- health

Future Trunks(DB Super)- stamina

Cabba- ki

Bojack- damage

Fused Zamasu- health

Dabura- damage

Android 17(DB Super)- speed

Fu- damage

SSGSS Gogeta- damage

SSGSS Evolved Vegeta- damage

Android 21- ki

G.O.D. Toppo- damage

SSJ2 Caulifla- damage

Dyspo- speed

Gamma 2- orange

Power Awakened Piccolo- ki

Android 18 (DB Super) - damage

Videl (DB Super) - damage

Broly (Restrained) - damage

SSG Vegeta (Ultra Supervillain) - speed

Rosé Goku Black (Ultra Supervillain) - stamina

Goku(mini/Daima) - speed

Belmod - ki

SSJ3 Vegeta - ki

SSJ4 Goku (Daima) - orange

Jiren(Ultra Supervillain) - damage

Final Form Mira- damage

Fused Zamasu (Half Corrupted)- health

Demigra- ki

Golden Frieza(Ultra Supervillain) - ki

Broly(DBS) - damage

An element of theming also exist in this buffing system; supervillains, saiyans, and androids will most likely have damage. Healing or ki assists mostly come from characters with a penchant to protect something. Burter and Dyspo have speed obviously

• 25% boost to all damage per ally assisting
  
  
• When user hp is below 25%, 15% boost to defense
  
  
• Limit burst revive gauge auto recovery

With this, damage assists become irrelevant in my opinion. Because you will get a larger damage buff from any and every assist.

CACs, Goku, Pan, SS4 Gogeta, and GT Goku all can use this super soul.

• 10% increase to the strength of whatever assist buff(s) you receive
  
  
• Limit burst revive gauge auto recovery

• Activates health auto recovery for all allies and you when using Hero's Flute
  
  
• 5% increase to defense
  
  
• Limit burst auto health and stamina recovery

https://steamcommunity.com/sharedfiles/filedetails/?id=1272407128
Pretty solid guide on the general foundation of team play in Xenoverse 1/2.

In crystal raids 9 times out of 10, raiders clap the whole team easily and that's in regular raid matches. Then there's double crystal raids. https://steamcommunity.com/sharedfiles/filedetails/?id=3139882500
Crystal raids could be a fun way to make regular use of this assist mechanic in mass.

When the Raider ko's all but 1 player, that last player can potentially become as strong as the Raider(or stronger in a downpatch). A bad player will get smoked regardless but a competent one can play on evened ground.

In PvE raids where people die easy, we could see new records in damage contribution if 1 lucky player with "Give me the power to take this guy down" was assisted by 2 people. Maybe not in overall damage but from individual scores we'll see new highs.

Want to toy around with this? Let me know cause I would too