This is by design though isn't it? Divine provenance is the alternative version of inquisition (like all other classes there are 2 spells that are alternative versions and share the same reuse timer) I know the spells are quite different one is a buff and one is a heal but I'm not sure they should be on separate timers without making the change to every other class and their alternative spells.
Yes, it is by design. I can't say I agree with it, but then again raw healing is pretty much useless nowdays anyway, so I doubt anyone actually uses Inquisition over Provenance.
Splitting them would be nice, though. Just in case something changes in the future