In that case, since it appears that the Apple store refuses to honor your new iPhone SE (4 months old) warranty, I suggest "calling" Apple and having them replace it via mail and also report that particular Apple store for not following Apple warranty procedures.
Apple wouldn't start working on a phone only to realize that after they had it apart it was a refurbished phone. Any Apple store I've been to would run a diagnosis check BEFORE they even check the phone in for warranty.
At least that's how it's handled in North America. Where are you located that this process didn't happen and they simply started working on your phone without any pre-inspection check in.
They did connect it wirelessly and do a diagnostic check on it first, first time over the phone, and the second time in the store.
And I am in Hampton Roads area.