[@Psyga315]
Basically depending on what the first event is that makes him have to use his Innocence on a new World, the abilities he has will stick with that Set until he leaves that World. If he's returning to a World he's been to before and he had Set 1 when he was there last, there is a chance depending on the first event upon returning that he will unlock Set 2 as it is the evolution of Set 1, however once he has Set 2 on a World, that will never change. 

The reason for this is that there are a few powers Allen actually loses when he gains Set 2, for instance the ability for his left arm to transform in size and shape as a claw, as well as losing the ability to shoot Palings and have a laser-sword. Also, he'd be a little OP if he used Set 2 all the time, as the difference in the power of the skills in each set is exponential. 

If the first event he uses his Innocence for involves an Akuma or other enemy that is a Level 3 or above, he will start with Set 2 in that World automatically, otherwise it depends on the individual situation. If the event is something like saving someone from falling off a cliff, he could use his left arm and start with Set 1, or he could save them with Clown Belt and start with Set 2.