My big question is "who's permission did they need?"
If ATC has gone home does the airfield not revert to uncontrolled procedures? I don't know EPZG but I did used to operate every day from aerodromes outside their ATC hours as well as completely uncontrolled aerodromes (IFR and VFR).
I would imagine they either departed VFR and picked up their IFR route clearance on the climb, or got the route clearance on the ground by phone or radio contact with an ATS.
Doesn't sound like anything was wrong to me...