Yes, like I said. Because you don't level up as adventurer, chances are 100% that a trophy will be a new class. Trophies only come from special monster kills, I thought that was given knowledge, sorry :D becomes fairly obvious after the first 2,3 trophies that they only drop from special monsters. Can be any kind of special monster though, and it still drops randomly. Again:
But will I unlock other classes this way?
If you only want to unlock classes as fast as possible, play adventurer.
If you don't care about "fastest", play whatever class you like, you'll level up that class AND unlock classes, and also get better scores. (because the other classes are definitely better :P )