Handicap based on which colour tee?

General Discussion
#1

All I read about WHS and Club handicaps, using the average of the best 8 from 20, refers to the “handicap” that your club issues?
Players A, B and C, all submit identical cards but play Blue, White and Yellow tees at the same club.
Hopefully the club allows for the difficulty in longer tees.
But when player A, who uses Blue tees, plays in a competition where they are all playing off white, has an advantage?
Likewise, player C, using yellows, finds that his handicap and any adjustments through slope or course, does not give him an equal chance to player B, who uses Whites?

So, my question, is how do the clubs determine the Handicap index if players use different color tees when accumulating the 20 rounds?

#2

Each colour tee has a different slope rating I think. If you play off a more forward tee your daily hcp goes down or of a tee further back you get more stokes. I think if I play off the ladies yellow tee my 14 hcp becomes the equivalent of 10 for the day. if I go back to the blue tee I go up to 15. This supposedly evens everyone out.