This happened to me as well. Just had to delete the iCloud one and leave the one with the Store Apple ID set properly. The only downside is, is that the profile pic is just my initials. There appears to be no way to set your profile pic unless I set up an iOS device with my iTunes Store account AS my iCloud account temporarily. Too much hassle.
Once and for all, Apple, please let us just merge Apple ID's....I'm forever cursed with my long history of purchases under an old Apple ID, and a newer separate iCloud ID for everything else.
I tried setting the image on iCloud Web, but it looks like it's not updating.