Well I didn't watch you put it on, so this might not be the case, but I've found that even if my sister's nails aren't 100% dry yet, I can still get away with using the top coat if I apply absolutely no pressure and just use the brush to lightly spread the polish (rather than applying painting-pressure).
Making sure you apply almost no pressure will also keep the coat underneath from re-wetting and transferring. (We use Sally Hansen and Julep Matte topcoats... Not sure if that information will help)