Tell your players what's in it for them.
As the GM it may seem odd to you to bring your players into the business of "rules enforcement". That's your job, right? But in this case what you want to do is better conform to an external set of guidelines; it doesn't particularly violate your authority to ask other people to help you run your game the way you want to.
Conveniently, Fate offers several built-in hooks that mean that when your players are helping you to work along with the guidelines, they're also seeing benefits for themselves.
I'm not going to give you a script to read to your players or anything; instead, I'm going to direct the bulk of the remainder of this answer to your players, and you can convey it to them as you'd like.
How Players Get Fate Points
Everybody loves Fate Points! They save your bad rolls and make your good rolls great. Wouldn't it be great if you could get... more Fate Points?
What if every time things got worse because of one of your character's Aspects, you got a Fate Point? Well, great news, that's called a compel and it's something your GM wants to do more of.
What if you had an idea of how things could get worse because of one of your character's Aspects or a scene Aspect, and if your GM agreed with you, you got a Fate Point? You're going to love this thing called compelling your own character. (And, just between us, as long as it's not a PvP scenario, you can bring it up for other characters too.)
Okay, but maybe you're worried about getting complacent and you'd like it to be on a timer. Like, instead of their infinite passive supply, the GM put one Fate Point per player in a little dish in front of them and you only had a limited time before they'd all go away? I see you're already familiar with the scene pool. Whenever your GM launches into something that sounds like it'll tie your characters up for a while and they don't have the scene pool in front of them, ask them "hey, is this a scene?"
(Yes, seriously have the little dish. A little physical prop of some kind to hold the fate points in the scene pool is a great signifier and as long as it's unique in some way it's hard to forget what it's for.
While we're on the topic of physical props, have a look at a similar topic on ways to remind yourself of the available aspects during play.)
How Players Spend Fate Points
There's something in the way of just spending Fate Points whenever you want. You have to point them at an Aspect, and that Aspect has to make sense in the story as something that would help you do better.
Though this is following improv rules, which are basically - as long as you believe in what you're saying, it's good. Like, honestly believe, not just hope to get a bonus nobody calls you on. You want other people excited to believe in what you're saying, not wavering because it's obvious you're trying to pull a fast one. (And it's always more obvious than you think it's going to be.)
The thing about improv, though, is that it works better the more there is to work with. When you're going to do something and all you know is your own character, you have much less to work with than when you know the whole scene - the time, the place, the task, the things, the people.
So when you the player are about to roll those dice, pause for a moment and ask yourself "what do I know"? Every roll you're going to make is set up in a scene (or if not in a capital-S-for-game-mechanics Scene, at least in the story), so if you don't know the story, ask your GM to fill you in, and maybe fill in some of it from your end. You're trying to Create an Advantage of a Souped-Up Landspeeder for the upcoming Spacers' Cup? Secretly at night? Openly during the day? Hurriedly on the morning of? The more you know about the circumstances surrounding the roll, the more places there are to aim Fate Points at - and the more ways there are for Fate Points to get bounced at you.