[Raigen.Convict]

As seen here if used while total control is off, queen automaton can IGNORE the cooldown on sharp game.

[Trexmaster]

It might be casting Rose Trap, not Sharp Game. They both show up as the same thing in battle logs and don't share a cooldown. You should be able to confirm by checking its statuses as it shouldn't be hidden from you the caster.

[Neus]

It is probably using Rose Trap and Sharp Game in the same turn, yes.