Hi
Tamiya white is one of the best fillers, better to apply small amounts on something like the side of a #11 exacto blade or dentist spatula. Too large amount dries quickly and doesn't go into seams well, should remain very moist until deposited.
Finger application is just too difficult to get into only the target area, messy results are what you get. You can still save the model by scribing into the filler that got into surface detail areas, when it's fully dried.
Good luck with it.
Patrick