by sigmazero13
I think the rules are pretty clear on this. In fact, on page 15 of the rules (in both the original and revised editions), in the "Player's Turn" definition it even specifically says:"For example, a Tactics card that can be played “During your turn” can only be used by a player right before, during, or right after the resolution of his active Order card."
So you can definitely play such cards right after you are done, before the next player goes. And in this case, you were playing it in the MIDDLE of your order (as it seems you played it after the main effect, but before the supremacy), which is also specifically allowed.
The long and short of it is, your friends were wrong :) Point them to this definition on page 15, and I don't see how they can argue with it.