yeah, dont use that.... you want to just use a small ball peen or other SMALL hammer and tap it in and out. that will obliterate the new cups before they are in. i have an old socket i keep in the toolbox that is the same size almost the same size as the cup that i use to help push out old ones and in new ones. greasing it should almost make it easy enough to push in by finger, it is usually the old rusty ones that are a pain to remove.
Mine go in by hand. they don't just slide it, but need firm finger pressure to get them in on all four corners. The first time i did it several years ago, I "cleaned" them up with a dremel and a fine barrel sander, just to get the rust off and smooth the edges. Now with a light layer of grease, they slide right in.
It will probobly not be a problem (hopefuly), but that tells me the cups may have been spinning to the point of slightly enlarging the holes. Back when you smoothed the edges, do you recall seeing any burrs on the edges?