The rule is to always rename a file and move to the right folder once its processed.
Well, the obvious question (besides that raised by mandy in particular, about authority) is: what's the purpose of that rule?
Presumably, that rule wasn't put in place for no reason at all, but to solve a problem. I'll hazard a guess that the problem it solved was that people didn't know which files had been processed and which hadn't been, and that this resulted in either double work or work that didn't get done.
If the new hires solve that same problem in a different way, then what reason (and, indeed, authority) do you have to force them to solve the problem your way?
Basically, don't look at whether someone is following a "rule" blindly, but look at whether they are solving the problem the rule was put in place to solve.
There's a place where following a rule or procedure to the letter is appropriate, but I don't think just keeping track of which files have been processed is necessarily one of those. It might be beneficial to simply apply a bit of flexibility here, and at most, remind the new hires about why that rule is in place and that it's the recommended way to avoid issues which presumably have been encountered in the past. However, you leave the decision (and also consequences) to them.
If, on the other hand, the rule was put in place by someone organizationally superior to the new hires, then enforcing the rule is their job, not yours. If not following the rule that has been put in place (and presumably explained to them) causes problems, you can be sure that they will find out about it.
Either way, for you to blatantly and repeatedly tell your superior how they should do their job is rarely a great career move on your part. Telling your coworkers how to do their job might not be as much of a career-limiting move, but can very easily come across as at least arrogant. There's a fine line between providing help or suggestions to someone new to the job, and telling them how to do the job they were hired for without being asked. Mind which side of that line you're on.