You got it in one, if the cake is very moist then you should use a high quality cup. The thicker the cup the better when it comes to moist cakes. If your cakes come out of the oven and don't collapse then there is no problem with your mixture. I suspect the problem is with the cup being too thin, the moisture and steam is penetrating the thin paper cup causing it to come away from the cake. If your cakes have fruit in, like cherries or other moist fruits this can also have the same effect.