Finalist for fellowship at prospective grad school. Does this mean I'm admitted?
I am the Graduate Coordinator for a mathematics PhD program.  But even I don't know the answer to your question (except possibly if  I'm the one who contacted you...but I don't think I sent out any emails quite like that).  So I don't think that random internet strangers can give you a definitive answer.

It's clear that you haven't been admitted yet, or the Graduate Coordinator would have told you so.  As for "usually imply" -- I am not willing to go so far.  What I can say is that being informed that you are a finalist for the fellowship certainly increases the chances you'll get admitted.  But for instance this fellowship may allow the department to admit a student that they would not otherwise be able to admit.  In that situation you would still think that they would admit someone that they put up for a prestigious fellowship ahead of most other students, but there could be exceptions.

As my favorite Harvard Square chess hustler used to say, "Sometimes you never know."