I accidentally put my canned tuna in the fridge

It is perfectly safe. You've got a pasteurized product that is shelf stable while the can remains sealed. All you did was make it colder for a few hours. This is not a safety issue at all.

There are only a rather small handful of cases where refrigerating some type of food is potentially problematic. They generally fall into one of four categories:

• Certain lipids congeal or solidify when they get down to typical refridgerator temperatures. This can cause them to separate out if they are part of a soup or sauce (often forming a scum-like layer on top of the other liquids if stored in bulk), or to solidify and cause things to stick together. Usually this can be solved by reheating and mixing, but in some cases it can completely ruin a sauce or gravy.
• Similarly, how much salt and other solids you can dissolve in a liquid is dependent on temperature, and chilling the liquid can cause such solids to crystalize or precipitate out out of the solution. This is more often an issue when putting things in the freezer, and can almost always be solved by reheating and mixing, but is a serious pain when it happens.
• A major component of perception of flavor has to do with olfactory perception of volatile (in the proper scientific sense of the term) compounds in the food. These compounds evaporate and disperse less readily at cold temperatures, so chilling certain foods can have a very significant impact on their perceived flavor. Famous examples of this include various varieties of wine and sake, which often taste noticeably different when served chilled compared to being served room temperature. In general, just warming the food up again will resolve this.
• Starch recrystallization, the primary process which causes bread and similar foods to go stale, happens more rapidly at typical refrigerator temperatures (as compared to room temperature, it actually happens even more rapidly at colder temperatures, up until you get to the freezing point of water, where it stops completely). This means that things like bread stored in a refrigerator go stale faster than they do if stored at room temperature (but, on the flip side, they generally don’t become moldy). Unlike the others, this process cannot be completely reversed.

None of these are really safety issues. All three except the last one might affect canned tuna, but I would think it’s unlikely to be a significant issue given that canning it in the first place already has a pretty big impact on the taste.

Lower temperatures result in less chemical reactivity and therefore less spoilage. In addition, the refrigerator, in principle, makes the space dry. All of these help improve the storage of food.

I don't believe that tin is used in the canning process these days, but I have heard this question before, and think that it may arise because of the use of tin in the past.

Tin and tin-coated steel has been used in the past in the canning process. Tin has several different crystaline structures that are stable at different temperatures. The atoms in the allotrope of Tin that is formed at 13.2C (56F) are packed less efficiently that normal tin, and thus the tin can crumble and corrode. This can cause damage to the tin can that could lead to food spoilage. This process is known as Tin Pest.

Tin itself is not very toxic, so any direct tin contamination would probably not be a concern. So in your case, even if your tuna can was made with tin, you'd be OK, and the short amount of time invloved means that spoilage would also not be a concern.