When I tap the ... button at the bottom of the iPhone App, then tap on My Reservations and again on Rooms and Packages, I get an option to link a missing reservation. When I tap on that "Don't See Your Reservation?" link, I'm promted for Confirmation Numebr and Last Name. It does not ask for phone number.
I remember there was a problem with an early version of the app that wouldn't accomodate linking resort reservations through your phone, but that should have been fixed (and has on my phone, as far as I can tell). Make sure you're using the latest version of the app.