It sounds to me as though there is a problem with your expectations that precedes the problem with their motivation. Your first strategies should be ways to address that.
You don't expect very much of these employees. To be precise, you expect more of them than you're getting, but you do so quietly. Your quiet frustration is no use to them and will not change their behavior. You say you don't want to resort to a formal procedure, but you must decide what your expectations are and communicate them to the employees. So, if these employees need detailed instruction then give it to them. And instruct them how you want them to behave, not the bare minimum you'll accept.
When you get that far, it would not be fair just to say, "I want you to show more initiative and be more committed". That is not a specific measurable goal. Neither is it fair to say, "balance Facebook use in a professional way" unless you're prepared to give guidance what is and isn't reasonable (and clearly you think their current level of use isn't reasonable). You also cannot expect everyone to invent work for themselves and review past projects all the time - some people can, but you must be prepared as a manager to give those who need detailed instructions enough work to occupy their time.
if I ask anything like "Didn't you think that adding this here would
have made it even better?" they answer "But that was not written in
Asking someone whether they thought of something is not the same as telling them that part of their job is to think of it and do it. Always be clear when giving instructions, that you are giving instructions. Be polite of course, but do not be indirect. It may be obvious to you that you're just being diplomatic, I promise you that the same is not always obvious to the person you're being diplomatic with. To them it genuinely might just sound as if they were asked to do one thing and then asked why they didn't do something different. Confusing.
If it comes down to it, write down in the instructions that you want them to give their opinion whether there is anything that could be added to make the output better. Then at least you can work out whether they thought of the same thing you asked them about, but decided not to do it, or if they just aren't very imaginative/confident/well-informed, or whatever else it takes to suggest improvements to their instructions.
Junior employees in particular don't automatically know how to judge when they should question the instructions they're given and when they should assume the person who write them knows best and follow them to the letter. Once those patterns are established, they stick.
If their performance is "fine" despite you giving them an amount of work for the day that they can complete in 2 hours between 3pm and 5pm, then you are not challenging them and you're not taking advantage of their capacity, but you are creating a pattern for them to fall into. Of course they aren't motivated.
Either give them a day's worth of work every day, or give them their usual 2 hours work at 9am and tell them to do as much of it as they can by 11. Then they have the opportunity to get themselves a thumbs-up at 11 by having it substantially finished, and an opportunity for even more recognition when you ask them at 11 how they can improve on what they already have. Also give feedback at 11 on what they're doing as they're doing it, before the deadline, instead of only in retrospect. All these things will make it easier for them to get motivated.
Once you establish your new expectations, you may find that you don't need to manage them very closely in order for them to continue in the same way: get their task done, deliver it, and only check Facebook while they're waiting for more work to arrive. Then you can work on getting them to show some initiative during that time instead of checking Facebook at all...
Now, it's possible that these people fundamentally want to get away with doing the minimum work they can, and they don't care about your expectations as long as they don't get fired. It's also possible that they just don't feel like the job is asking for their full attention and commitment, and will give those things when they're demanded. You will not find out which until you sort out your side of the equation.
You said in comments:
I personally grew up with an attitude that if I have to focus on
something, everything else has to wait. It's discipline, and
discipline helps me focus. Why can't others just follow that simple
Others are not you, and you cannot manage them by expecting them to have the same attitude you grew up with, or behave as you would. The closest you can come is to state your principles and require them to follow them -- that is to say, tell them not to do (so much) personal stuff at work, and give them something productive to do instead. But normally you don't need to spell out your personal path to self-discipline, because the techniques by which each employee stays focused matter a heck of a lot less than whether they feel they need to be focused in order to do what's expected of them.
Bear in mind also that different people are productive under different conditions. If you can focus on one task indefinitely to the exclusion of all else, then good for you. Others do not share your superpower. To them it is not a simple principle, it is a physical impossibility.
Likewise there are people who clear their to-do list and then take a break, and there are people who wait until their to-do list is urgent and then do it. Long-term you can talk about attitudes and discipline, but the easiest way to make the latter behave like the former is to set shorter deadlines ;-)