32-622 tire too small for 622x19 rim?
You have the correct tires.

This does not have anything to do with tire width. The diameter determines whether tires will fit or not, unless there is a huge width mismatch. Rims and tires are both made to a tolerance, and you just happen to have an unusually large rim and small tire. I have had the opposite problem with some Schwalbe tires, they were so loose that they kept slipping off the rim when installing.