There's pretty much no clear cut rule, as far as I can tell, and you tagging it for effect when appropriate seems logically fine.
For instance, you shoot someone in the arm. They get the aspect "shot in the arm" as a consequence. They go to shoot you (same exchange, you've already gone). Nothing keeps you from tagging the consequence right then to have them automatically miss (unless they spend a fate point).
I used a different example because, in yours, the guy with the "knocked down" tag on him shouldn't, system-wise, be able to just run off without removing the tag. I mean, it's kind of an unopposed action to stand back up (athletics), so removing the tag is quite easy.
So in game terms, he's removing the tag with an uncontested athletics roll (no real need to roll), and he's taking a move action as well (which would give him a -1 to the athletics roll, if it was really needed). There's absolutely nothing that I can find preventing you from tagging that for an effect like him tripping as he tries to get up (unless he spends a fate point).
Actually, from most of the examples it seems you pretty well are fine to do this. I mean, any time you invoke your own aspect reflexively in defense, it's not your turn.