Just got my gold 5s w/matching headphones to replace my 4s in the other day... LOVE it.
Come at me android fanboys , you're rocking a STOLEN os paid for in billions of dollars in nickels, lol google that shit.
Anyways, back to the subject at hand. What Daisan said about multiple devices/automatic downloads is true, if I add/remove a device I usually collect them all up check settings and sync.
Out of curiosity, did you delete the app on your CPU before deleting it on your phone?