You know for a fact? How exactly? No offense, but I'd like to see some proof if you're interested in providing it. All you need to do is go into the game, press "P", find the powers you mentioned and select them. You'll get a dialogue telling you exactly which skills modify each of the abilities you mentioned. Is "Starship Engineering Training" actually listed among them? I think you're going to find that the answer is "no".
I admire your skepticism. Luckily, there's an easy way for you to check this out without having to get a bunch of engineer BO's into a higher level ship to check the "P" menu. If you go to the BO requisitions vendor in Earth Spacedock or bring up the BO's in the exchange, you can right click on the entries and see the full, detail "P" menu tooltip for every abilities those officers have. Checking this, I confirm that Directed Energy Modulation is affected by Engineering Training, as is Auxiliary Power to the Structural Field (I was strangely unable to find any instances of the Auxiliary Power to X abilities, has anyone seen these? At any rate, I find it likely that they follow the same pattern as Structural Field), while Extend Shields is not affected by Engineering Training (It is affected by Warp Core Training instead), and the tooltips for Aceton Field, Eject Warp Plasma, and Reverse Shield Polarity are sadly lacking the skill information. Since Eject Warp Plasma is specifically called out by the tooltip for Starship Engineering Training, it is probably safe to assume that it is in fact affected by that skill. This leaves Reverse Shield Polarity and Aceton Field as question marks until someone can check them (which will be quite difficult for Reverse Shield Polarity, since the tooltip gives no feedback on how effective it is).
At any rate, we can say with confidence that the following skills are affected by Starship Engineering Training:
Eject Warp Plasma
Directed Energy Modulation
Auxiliary Power to the Structural Field
Rotate Shield Frequency
Along with hull repair rates. I suspect that at least one of Reverse Shield Polarity and Aceton Field are affected by Starship Engineering Training, if only because if both of them are affected by Warp Core Training, that leaves the majority of skills affected by a skill that is already highly useful for its own sake for improving power levels.