Nah, it wasn't a Mustang or Spitfire, and I'm only assuming it was a 109. It was painted up in WWII Luftwaffe livery. It had a much lower revving engine than a Mustang or Spitfire if that's any help.

There was a historic war plane air show recently in the South Island (Warbirds over Wanaka,) so it may even be a visiting plane doing the rounds in NZ as I haven't seen it before here in Tauranga.