There is too little information for a definitive answer; for example, I don't know what kind of plastic it was. However, I suspect it was not a chemical reaction, but plasticisers in the plastic that dissolved the plastic enough for it to soften and merge.

A plasticiser is a chemical, a sort of mild, non-volatile solvent, that gets between the chain-like molecules of a hard kind of plastic and stops them from sticking rigidly together.  Different kinds of hard plastic largely need different kinds of plasticisers. If the molecules of plastic cannot jam hard against each other, the plastic remains soft, more plastic; it will not easily crack, for one thing.

There are a lot of technical problems with this principle, but one of them is that your soft, plasticised plastic can stick either to other pieces of the same material, or sometimes other materials. For example, PVC is a plastic that has been used in many, many applications with lots of plasticiser. You will have seen clear PVC envelopes that we use for saving printed pages. They are popular because they work very well. However, if you use them to keep sheets of paper that have been printed by laser copiers or printers, and you leave them in storage for some weeks or longer, you find that the ink sticks to the envelopes so hard that they pull it off the paper. The problem is that the ink is a plastic that dissolves in the plasticiser. It is as though you had placed a soft jelly in contact with sugar. The jelly might not look wet, but the sugar does absorb its water and then it sticks.

So, as I said, I suspect that your dishes were plasticised, and that they fused slowly on contact.