There's no distinct fare class for premium at this time. It's just about the seats. You have to set your own reminders for your upgrade window to determine when its free vs a paid selection.
I do, however, use EF to set "seat alerts" for premium seats though, particularly if I"m waiting to be upgraded / none are available. If people get upgraded to F and their seats become available, you can snag one a bit easier that way without having to go in and check the seatmaps constantly. You can set those from viewing the seatmap, setting a seat alert (be sure to check the paid/premium boxes so they notify you on premium seats too, not just standard Y), and then select certain criteria or specific seats. If you haven't already setup EF to email your carrier's email equivalent of your phone number (so you get a text), I'd highly recommend that too. Closest thing to a push notification you can get, at least until TPG's team makes EF an app and offers that.