PVC reacting or self-decomposing?
What you are seeing is most likely PVC plasticiser.

Pure PVC is a hard, inflexible solid. It doesn't make for good flexible objects. To make it flexible, plasticisers are usually added. These plasticisers are often compounds like diisononyl phthalate (DINP), diisodecyl phthalate (DIDP) and di-2-ethylhexyl phthalate. These are, when pure, oily liquids. They often slowly migrate from the PVC object and can do so faster in certain circumstances (eg they will be pulled out when the PVC is in contact with hydrocarbon solvents).

So, most likely, you are seeing small amounts of plasticiser migrate from the PVC and not any degradation of the polymer itself. Eventually, of course, if enough plasticiser leaves the PVC object it will become brittle and inflexible. But it may be quite some time before that happens.