Ok, something has to be really seriously messed up for the pitch difference to be a semitone I measured it on my bass just now and it was only 13 cents. Maybe tailpiece, maybe soundpost, but something is not right (and seriously so intonation changes mean something structural is shifting).
While it is true that the effective length and mass may change, I'm sure that's a very much smaller effect than the tension increase. You can't see the strings move over either the nut or the bridge, and they'd have to move by a reasonable fraction of a millimetre to have any appreciable effect.
I mistyped that. It was at worst nearly a 1/4 tone, but usually less than that.