I know it appeared before he wore it, but it was HIS costume, and he did wear it, so I'd say it was his.
IIRC He loans the Adams costume to E1 Robin because E1's costume was badly torn (Yum!)
Also, I can see E2 Dick perhaps being a little hesitant to wear what is essentially an update of his old costume after he's gone to all the trouble of designing his own (hideous to be sure, but his own) not-very-like-his-Robin-gear outfit. (Also possibly embarassed that he'd have to go back to Adams to get the costume let out, since, as you say, it fit E1 Dick like a layer of spraypaint!)
Later on he caught sight of himself in a mirror (possibly after getting contact lenses) and went "Ye Gods, I've been wearing THIS piece if shit as a costume? When I could look like a slightly more mature version of E1 Dick in a snazzy costume? No contest!")