If the resin is not hardening and seeming gummy then something isn't right. If it is hardening but remaining slightly tacky, then it could be within the realm of 'normal'.
I'll give you a quick solution, and then provide you with an explanation of the problem. After curing the resin with your UV light give the cured resin a quick wipe with an alcohol swab. It will remove that tack and you'll be left with a smooth, hard, clear cure.
The tack that you're experiencing is the result of "oxygen inhibition", which is a fancy way of saying that oxygen inhibits the outermost layer of applications of UV-curing resins to fully set up. In other words, the application should be cured all the way through, save that outermost layer that still feels tacky. If you picture a cross-section of the resin, then imagine it curing from the inside out. The outermost layer, which is exposed to the ambient air, may remain tacky even though the rest of the applied resin is fully cured.
Because UV resins behave differently than traditional types of cement, the amount of time that they are left to dry won't benefit either the strength of the cure or the tackiness.
In our experience in using developing and using other resins, a tack-free cure comes at the expense of durability. In other words, the resins that we've experimented with that solve the tack issue are brittle and don't hold up well when fished.