Are you finishing in the Murkwood Arena (PVE) or regular Arena (PVP)? It won't award in regular Arena, even though all the other activities for Murkwood Arena also progress when you're doing regular Arena.
Having the exact same problem. I complete a "place top 3 in Murkwood Arena" task, but it just restarts and gives no tickets.
If you refresh the page, you don't visually see the pop up with the
tickets being added and a new game will be started, but they are awarded
to your account. If you specifically want to see the pop up you have to let the battle play out.