I've never had any problems with Tamiya's enamels or acrylics. Make sure you're using the appropriate thinner. (X-20 for enamel, X-20A for acrylic)
I have no idea what effect using the wrong thinner would have, but that might be it.
Tamiya's acrylics dry lightning-quick, especially when airbrushed.
Your comment that the paint remains sticky sounds like what happens when enamel paint is applied to vinyl. What type of material did you paint?