I just leveled up a heroes costume that is in my raid tournament. I only got the costume this week during the costume chamber quest so I had not had it when I set my defense. Specifically, it is boldtusk.
So, I ascended the costume to tier 2 and my hero in the tournament got a boost. I did the same to tier 3 and it happened again. It appears the costume bonus gets added if the changes occur post the tournament start. I’m thinking this may be a bug.
I leveled troops last tournament and they did not get a boost. So it appears odd that the game would let one thing happen but not the other.