It took me a while to figure this out too. You need to download the Playstation Mobile app at http://www.playstation.com/psm/store/en.html
(I know you already have this. I'm just helping others who might be confused.) and download the games through that app. I was trying to download the games through the Playstation app that came with the phone.
Not that you care, but my phone history: Samsung SGH-N105, SGH-S105, Sony Ericsson T68i, Nokia 3650, 3220, Motorola SLVR L7, Blackberry Pearl 8100, original iPhone, 3G, 3GS, & 4, Samsung Galaxy SII Skyrocket, SIII, Note 2, HTC One, LG G2 & Pebble watch, Sony Xperia Z2 & LG G Watch (current)