This is another one of those areas in which the system leaves it up to the table to decide how to apply the mechanics. Yes, the GM can simply decide to compel NPCs on their consequences without input from the players. Yes, the players can suggest that the GM compel the NPCs on their consequences without paying Fate. And yes, the players can tag or pay Fate to invoke those consequences on their own.
My thoughts run along the following lines:
If it seems clear that a particular injury (as indicated by a consequence) *should* lead to a some difficulty (compel) most or all of the time, then it probably shouldn't cost the players a tag or a Fate point to trigger it. For example, if an NPC has a Broken Leg and tries to jump across a chasm, then the GM probably ought to run the compel 'for free', whether he thought of it or it was suggested by a player. The result *might* be that the NPC pays a Fate point to ignore the compel, but the compel should probably happen.
On the opposite extreme, if a consequence *could* lead to a particular difficulty, but only with a considerable amount of unluck, then the GM should probably only run the compel if the players trigger it via a tag or Fate point. For example, if the same NPC with the broken leg wanted to hobble a few yards around the corner of a building, using the wall as a support, then its reasonable to assume that the action would normally succeed ... unless "something goes wrong".
How to adjudicate this? Well, at the risk of being vague, I'd say that if a player suggests a compel, and you immediately agree, then run the compel on your own dime. If you don't think the compel makes sense at all, then just say 'no'. And if you are pondering whether or not the suggestion is truly compel-worthy, then hold out your hand and wait for a Fate point to materialize (or a tag to be used). So yes, it's basically a judgement call.