You can get xp elixirs from the silver and gold elite runner chests. I think silver might have a slightly higher chance. Lots cheaper than the full elixir and if you have all quests ready to turn in, 10min is more than enough. Usually 3min is more than enough. It takes me less than 10 runner chests to get an xp elixir.

Other than a few quests in zones, most quests do not tick the xp elixir. I can only think that you had a ticking elixir (from Shazbot or Klaas) and your other elixir did not override it, so it was still the free ticking elixir. Anyways, make sure to check before popping any elixir.