How can you make reloads without owning a set of calipers?
But anyway, it sounds like either the bullets are not wide enough or the cases are being sized too wide. How come you keep insisting that the cases are in fact sized correctly if the bullets slide in with just a bit of a tap? Again, for that to be possible, you have to either have the cases too widely sized or the bullets can't be the correct size.
Lastly, and perhaps of most help to you is that you are not crazy or imagining this. It is probably really happening. Bullets can be mislabeled by the manufacturers. I've seen posts over the years where people report getting incorrectly labeled bullets from well-known manufacturers. It sounds like either your cases are being sized too widely, or, maybe more likely, your bullets are actually 9 mm, incorrectly labeled as 38's.