Is your unit a 3 way, or is it only DC and Propane
? I'm assuming it's an absorption unit because of the propane
AC, DC or Propane, absorption refrigerators operate based on heat; AC and DC via a resistance heating element, propane by a small flame. In any case, it takes some time to cool the unit.
Recommended practice is to cool the unit via AC for at least 24 hours before putting pre-cooled items in the reefer.
I don't know that there is necessarily a problem with the AC converter being in battery charge mode, as the reefer will draw what it needs, probably 10 amps or so and allow only what is left over to actually go to battery charging.
Final note, absorption refrigeration is less effective when external temps are 80 degrees F or greater. An added fan to pull heat off of the coils is a good practice. I'm getting ready to add a second one on my unit.