The glue turns to a blue/green jelly when the Autoglym has finished working.
You then need to do a lot of rinsing and I always give the whole thing a wash in diluted Fairy liquid to get rid of grease.
Then I condition it and let it dry naturally.
Using the microfibre cloth and the fine tooth comb to remove the softened glue really helps to declump the hairs.

It does sound like you need a bit more practice with glue.
You shouldn't be getting it on your fingers and its possible you're not letting it dry fully before attaching, hence getting the hairs stuck.

But I think some people are tape-people and others are glue-people!
I'm ok with glue, but I remember getting in a terrible muddle fiddling around with bits of tape.