So short answer is no you don’t have to provide proof; you keep track of the hours yourself and report it on your application. You do have to provide contact information for a reference (which can be anyone from the organization that can verify you did work there); in theory, medical schools could contact that individual to verify but in practice they will not do so unless they have reason to suspect you’re lying.

So long story short: no you don’t have to save anything to provide proof except for a valid contact from that organization; if you report 148 vs 150 hours no one will care, so don’t overthink it just keep track of the hours yourself knowing you’ll need to report them later (I.e. don’t stress if you did 52 minutes and you record it as 1 hour, if that makes sense).