Printing UV on plastics is a common practice but different plastics behave differently. In Dry Offset, it is common to print these cups but the surfaces usually need to be treated. This is usually done with flame treating but some times with corona treating.
Normally surfaces of plastics can be measured with a Dyne test. Some flat sheets of plastic might have enough surface treatment still remaining from the suppliers process. Too much treatment can also be a problem. Over oxidizing the surface can result in a weak bond because an oxidized surface, which might measure high on the Dyne test, is like putting paint on a rusty (oxidized) surface. The flame on a flame treating station can be a "oxidizing" flame or a "reducing" flame. This depends on the ratio of gas to oxygen in the gas/air mixture. Some plastics are sensitive to this ratio.
Sometimes the adhesion will seem to be good but if exposed to wet conditions, the print can fail and come of the surface quite easily. This needs to be checked.
Primers have also been used to improve adhesion.
From what you are saying, it does not seem like you are really printing on metal. Printing on metal is also common but I do not know what is required for the surface conditions.
You say that the metal you are trying to print on has a Thermoset surface. I guess you are talking about some plastic coating. This too needs to have some adequate surface treatment too. Smoothness is probably not the issue, since basically adhesion is mostly a chemical problem.
You need to get some information of the surface conditions of that thermoset coating. Good luck.
