There is no in-game indication that this mod is installed. (i.e. there is no mail, etc.) The only way to find out is to fight The Brotherhood again or check the server's mod list.

The exact mechanics of how these guys work:

• The first fight goes as normal.
  
• On the second and subsequent fights:
  
  • Two new enemies spawn - Flare and Wastelayer.
    
  • Flare has a laser script similar to IDHTX. It uses turret-based lasers as a primary weapon.
    
  • Flare is guaranteed to drop an exotic laser.
    
  • Wastelayer will continually fire torpedoes at a randomly chosen enemy and uses chainguns as its primary weapon.
    
  • Wastelayer is guaranteed to drop an exotic chaingun.
    
  • All members gain the "Avenger" script and the remaining members will gain a damage buff whenever one is killed.
    
  • All of them gain the following multiplier to durability - [Base Durability] x (1.5 + (X / 4) + Y)
    
  • All of them gain the following multiplier to damage - [Base Damage] x (2 + (X / 4) + Y)
    
  • X is # of kills - 1 (maximum 10)
    
  • Y is # of kills - 10 (maximum 15)
    
  • Tankem gets a better damage / durability multiplier than the others.
    
  • Reconstructo gets a slightly better durability multiplier than the others.
    
  • Damage / HP boost caps at 25 kills.
    
  • This means that the durability caps at x19 and the damage multiplier caps at x19.5.
    
  • Reconstructo gains the allybooster script and will buff other members.
    
  • Whenever another member is buffed by Reconstructo, they will be healed for 33% of their durability.
    
  • Hullbreaker and Shieldbreaker gain the overdrive script which will occasionally give them a boost to their damage.
    
  • Tankem gains the adaptive defense script, which will allow it to adapt to whatever damage type is being used against it.
    
  • Tankem gains the iron curtain script, which causes it to become invulnerable for approximately a minute after reaching 25% HP.
    
  • The pre-fight dialog is different.
    
  • The boss music is different. You may recognize it if you're a Nier fan.
    
  • The loot dropped is better.
• On the third and subsequent fights:
  
  • All of them gain a jammer script.
• On the fifth and subsequent fights:
  
  • All members gain a more powerful jammer script.
    
  • Hullbreaker and Shieldbreaker gain an additional +25% damage multiplier - this is multiplicative with the base formula mentioned earlier.
    
  • Tankem gains an additional +50% damage multiplier - this is multiplicative with the base formula mentioned earlier.
    
  • Reconstructo gains the eternal script, which allows it to self-heal.
• On the tenth and subsequent fights:
  
  • Wastelayer and Flare gain the overdrive script.
    
  • Tankem gains an even more potent jammer script.
    
  • Tankem gains a special script. This script adds a seige gun script to tankem, and allows it to become invulnerable for approximately 2 minutes after reaching 35% health.
    
  • Reconstructo's allybooster script buffs / heals every 30 seconds instead of every 60 seconds.
• On the eleventh and subsequent fights:
  
  • Wastelayer's torpedoes now do four times as much damage and are twice as durable.
    
  • Flare's laser now does twice as much damage.
    
  • All of them drop better loot.

Each time you kill them, a counter is incremented. This does not affect all players on the server - the # of times killed only affects how strong they are for the player who is spawning them.