The one thing I've noticed a couple times immediately after putting a new chain on a used cassette is a mechanical vibration with a slight associated noise like a whirring. It's reasonable to assume it the slight mismatch between new chain and old cassette. That might not be what's actually happened but my interpretation of it. It passes after a couple rides, presumably as the chain meshes. Could that be what is being reported ?
Alternatively, the transmission is a relatively simple thing, if there were no noise, no cause to assume there might be maladjustment before the change, it's reasonable to assume the cassette is worn then...and change it.
In my humble opinion, theres often discussion about when, how to know when things should be changed, chains particually. These are consumable items, they dont last forever, personally I'd just change it. Realistically, if it was fine before, theres only really two things to consider.