the door does not have self closing hinges but it does have a screen door closer. Is this ok or do I recommend that be replaced with self closing hinges?
Are you referring to your local area fire separation requirements?
If so, what protection against fire would a screen door closer provide?
Yes and the closer would close the garage man door not prevent fires only keep the fire from the house. I have never seen a garage door with that type of automatic closer only self closing hinges. So is the door closer ok or should I recommend the self closing hinges.
You are asking whether a screen door return spring closer is OK to use on an attached garage fire rated door into the house?
If it fully closes the door it is OK, and may even better than spring hinges, which often don’t pull the door fully closed and latched.
The only door that matters is the fire rated door. I always suggest spring hinges.
If memory serves, the “requirement” for “self-closing” doors ended with the 2006 Code cycle. That does not stop me from recommending them on virtually all homes ever built!