Try googling for 'anki midnight' or 'anki timezone'. http://ankisrs.net/docs/manual.html :

The Next day starts at option controls when Anki should start showing the next day’s cards. The default setting of 4AM ensures that if you’re studying around midnight, you won’t have two days' worth of cards shown to you in one session. If you stay up very late or wake up very early, you may want to adjust this to a time you’re usually sleeping.

Mnemosyne has the same thing, although I don't think it has the Anki (mis?)behavior of adjusting for changing timezones.