Can canned food (like tuna) be refridgerated for months then put back in the pantry

Two problems:

1. Hot or warm food will briefly warm up the air and therefore to some degree the food already in fridge, especially items immediately near it. Cycling temperatures does not help fresh food quality or life. Modern fan forced fridges may suffer this problem less.

2. It is very power inefficient to do this. Just let it cool on the bench until it reaches a cooler temperature and then place it in the refrigerator. Use any of the well-documented and appropriate techniques to cool food quickly and safely if it is going to longer than 2 hours to cool.

As far as I know, raw tuna is not usually salted and/or pre-treated.

What may be happening is a case of perceived salinity. For example, there are numerous studies that suggest foods with certain odors can be perceived as much saltier than they actually are. If you have access to that second article (it is copyrighted and behind a paywall, so I can't post it here), it has a great figure on page 3 depicting the perceived sourness, bitterness, sweetness, and saltiness of a number of common foods, including tuna. The aroma of plain tuna alone ranked higher than soy sauce on the saltiness scale, for example. Tuna is relatively high in fat, and other studies suggest that high fat foods can also increase perceived saltiness. Perhaps you were using a fattier part of the fish?

Finally, there is evidence that dehydration increases the saltiness of tuna (which actually seems somewhat intuitive), especially if extra salt is added before cooking. Was your tuna previously frozen? Freezing—especially if done improperly and/or if there are multiple freeze/thaw cycles—can act like dehydration.