It’s a thin line. Instead of just throwing my approach at you, I will begin with a quotation of p. 281 of the Core Rules (emphasis in source):
When you [as a GM; annotation by MisterX] are framing a scene, it is up to you which Traits you establish affecting how the Player Characters will interact with the scene. Once the scene is underway, the only way to change thos circumstances is the use of Threat, or through the actions of Non-Player Characters.
This is very important: any change the Gamemaster wishes to make to circumstances once a scene has begun must come from either a Non-Player Character or from spending Threat.
My interpretation is this: Threat mechanics are there to let the GM be a player, too. The GM plays their own game, yes, with different rules and challenges than the players, – but the GM is actually bound by rules and is not omnipotent.
So, the moment a scene is set, the “I just describe everything that I think is cool right now”-power of the GM is gone and every change in the scene must stem from actions of Players, or NPCs, or from Threat.
Thus, I ask myself two questions, before paying (or not paying) Threat for NPCs joining a scene:
1.) Are they new to me, my plans, and my scene setup? Meaning: If I planned that the captain and another officer are in the ready room and I set up the scene describing not only the bridge but also this conspicuous door probably leading to said ready room – then they’re not new. They were, albeit hidden, part of the scene in the first place. If I instead simply describe the bridge and mid-scene come up with “oh, and by the way, there’s this door on the left of you all, it opens and, guess what, a Klingon captain and another officer storm out and join the fight” – yepp, gonna cost Threat.
In short: If there’s Chekhov’s Gun hanging on the wall, using it will most likely not cost Threat. If it doesn’t, I’ll pay.
2.) Are they a fundamental change to the scene? Let’s say the players beat all the Klingons on the bridge and combat is over – bringing in the Captain and the other officer would start a new combat encounter. That’s enough to change the scene, as it limits the Players’ opportunities to e.g. hack into consoles etc. Thus, even if the captain and the XO were there in the first place, I’ll probably pay Threat to bring them in just now instead of, e.g. setting up an ambush in the ready room or just conveniently having heard nothing, or whatever.
Having written all this, I can now boil down my approach to it to an even shorter thought:
If it’s a surprise for your players mid-scene, that is a good indicator that it probably should cost Threat.
It’s a thin line, though, that requires a lot of mutual trust betwen the GM and the Players. AND it has to work with your and your group’s view on the GM’s role. Right after my first STA one-shot I had a conversation with a Player I played D&D with for years. He opposed paying for reinforcements by Threat as he was of the opinion that, as GM, I was entrusted by the Players with the Power to do anything in the story. “But you’re the GM!”, he said, “Why do you need to pay to change the scene? Changing the scene is the GM’s primary job!”
And if that’s fine for everyone, than that’s that.
Long story short: Threat is meant to work as a dramatic story-telling-tool for the GM, both enabling and limiting them to change scenes they do not, just like the players, have total control over. If this is how you like to play. If not, houserule and maybe even don’t pay for reinforcements, ever. Your game, your rules.
