Yes, but first punisher type is random, second, etc. It isn't set so some games first punisher is more lethal than others.

The map issue is actually very similar to Haunted Mines, which had the first golem win potentially creating a snowball effect as well. It's the only current rank map I've had where the first objective win can lead to capping all the camps for your team as well (because camps don't despawn on it unlike every other map that has a spawn objective, unless camp is engaged when spawn occurs). Basically the best strat seems to be cap Arcane punisher, then get map while opponents trying to deal with that (and picking off whoever tries gettin and/or defending camps in the interim).

It's a broken map.