I'm running a tac officer in a tactical escort. I'm not getting much use out of my engineering boff's lieutenant ability, so I'm thinking of switching it for engineering team for the hull heal. However, I'm already using tactical team, and I noticed the wiki says they "share cooldown"? What exactly does that mean? Would using tac team trigger the full cooldown on eng team (or vise versa) or just the 15 sec one, similar to the way torpedo high yield and spread interact?
Shared cool down means that a similar set of abilities have a mutual cooldown if any ability of that set if used. What you are encounter is the Team skills cooldown. meaning it's you crew's efforts to do the task you told them to do. Similarly science abilities which use the Deflector Dish (i.e. Gravity Well, Tykens Rift, etc.). And as atillo mentions the Beam and Torpedo skills are another sets.
Game size the shared cooldowns is balance purposes. For example, being able to use Torpedo: High Yield, abilities back to back. Stack on Attack Pattern Alpha, Beta and Omega at the same time. Fire on my Mark. You could classify any target as vapor. There isn't enough defenses in the game to stand up to that for players nor NPCs.