In a situation where two opposing players have these abilities/ pilot is it initiative order that decides?

In the example I have asaaj has heightened perception and initiative, she chooses to activate it. However torkil art a lower initiative then activates and nullifies asaaj's power.

To me that looks like initiative is actually a penalty?

To use the current terminology, Player Order will decide the order in which Torkil Mux's ability and something like Heightened Perception or Roark Garnet. By 1e terminology, this would be called initiative. However, in the current edition, Initiative (pilot skill as was) doesn't factor in here.

Being first player or second player, in any case, has advantages and disadvantages.

What @theBitterFig said. Player Order determines resolution of all "At the start of the _____ phase" effects (first player resolves everything in their selected order, then second player, and so on if applicable), except for the System Phase, which has its own rules about order of effects (resolved by ship initiative first, then by player order in the case of ties).