I'm a Tactical Officer, and I put max points into Starship Engineering Training, Starship Warp Core Training, Starship Operation.
And I heard those skills are only for improving Active skills of Engineering & Science Officer.
God... Then Those passive skills are useless for Tactical Officer?
They are not useless for Tactical Officer.
The Warp Core training will increase the power levels of your EPS. It's probably the most important skill to max out of the Lt level skills.
Starship Operation, and Starship Engineering Training will effect your Science Bridge Officer, and Engineering Bridge Officer abilities respectively. Again this is rather important to increase as these skills are what will be used to save your ships life and keeping you from getting spaced.
I should also note that so long as the instance is not full, then it will be put at the top of the list. In addition, if they are in a different zone completely (Say, Earth system) and they zone to Sirius Sector Block, it will automatically attempt to put them in the same instance # as you.