Whether to tell my PhD advisor about transfer
Since you've already reapplied, you're best off waiting until you've heard from the other university. There's no point in poisoning your existing relationship, which would have been the net result of telling your advisor you've applied somewhere else, and then not gotten in.

However, have you had an open discussion with your advisor about why you want to transfer? Perhaps there's something that can be done to improve the situation—maybe a co-advising situation, or a transfer to another group at your current institution?