Parallax Scroll
Banned
The inputs issues exist in Vanilla too, sometime you'd end up doing a SRK Super with Akuma instead of the Hadoken one and it was a pain in the ass to burn your X Factor just to save Akuma.
Apparently this thread in Shoryuken has the solution(s) for the DHC input problem.
http://shoryuken.com/forum/index.php?threads/gimlet-dhc-input-bug.149514/#post-6148852
The specific post linked there seems to have it right. According to him, if the character starting the DHC does a QCF super with 10 or fewer frames before the super flash, you'll run into this problem. Here's his list of affected characters:
Jill
Phoenix Wright
Strider
Vergil
Wesker
Dante
Tron Bonne
Chun-Li
Felicia
Akuma
Haggar
C.Viper
Hawkeye
Doctor Strange
Iron Fist
Rocket Raccoon
Dormammu
M.O.D.O.K.
Spider-man*
Sentinel (both hypers)
Hulk
Super-Skrull
Phoenix
She-Hulk
Taskmaster
I tested the first 3 on that list (Jill, Wright, Strider), and confirmed that it works just like starting the DHC with Wesker. Delay the PP input on the first character's super and you'll be OK. Don't delay it, and you'll get an accidental DP super for the second character.
I also tested starting the DHC with someone not on that list (Ryu). No accidental dragon punches on the second character.