I often find people (mostly American people) telling to me "you will want to do this" or "you will not want to do this". Does it mean they are telling me that I should do something (in the sense of being authoritative) or are they just requesting that I do something?
It literally is a prediction of a future condition. It's often used as a way of sharing your experiences with the hope of those experiences helping someone else. It can be a way of insinuating commands or requests, but only as a turn of phrase.
For example, a person who just got out of the rain might tell someone about to leave that "You will want to have an umbrella." If a road is blocked, they might say "You will want to drive this other route."
By alerting someone to a future condition, you help them make informed decisions without stepping on their toes.
“You will want to do X” is simply an informal yet animated way of saying, “I highly recommend trying X.” It's usually meant to be friendly, more so than authoritative; the speaker is sharing heartfelt enthusiasm, often based on personal experience. For example:
You will so want to stay active on EL&U! They've got some great people there, and you can learn a lot.
In "American" it's basically saying: In my opinion this is the best course of action for you, you don't have to follow it, but if you fail I can say "I told you so"
It can be perceived as a way of giving advice, a way of trying to persuade someone of something, or simply as it is. "You will want to do this" could mean that the person saying it wants you to do this, believes that this is something you should do, or believes that, if you don't now, you will later want to do this.
The other side of all this is that if someone says "You don't want to do this" it means that either the person doesn't want you to do this, that the person believes that this is something you shouldn't do, or believes that this is something you will regret doing later.
They mean "the best course of action is to do..." or "what you should do is..."
Personally I find this phrase gets my back up, and thankfully I don't hear it much. It's purpose is to say at some future point you will agree with someones point of view, instead of letting the person in question room to make their own conclusion in their own time, and adjust their position.
The social norm would be to agree with the answer, alternatively try answering this question with a plaintive non-committal answer, like "okay, we'll see", and sometimes you may get the following response "No, you will!". Things could then become a bit confrontational, for a simple question like "Do you want Parsley on your soup?".
I'm not sure why OP says this colloquial use of "want" is "mostly American" - my understanding is it's primarily a British thing. Here's UK comedian Harry Enfield with his "Mr. Don't Wanna Do That" stock character.
I don't think there's any meaningful difference between present (don't=do not) and future (won't=will not) tense in this context, but feasibly some might feel that future tense is more "distant/oblique/deferential".
It's possible using "want" rather than "should/need" is partly motivated by a desire on the part of the speaker to downplay the advice/instruction overtones - but as that Harry Enfield skit humorously shows, patronising advice is patronising advice, whatever language you couch it in.
My own feeling is the usage is unremarkable in contexts where the speaker is recognised as an "authority" (in the sense of being expert, not dominant). Focussing on what the "trainee" wants to do, rather than what he should do, is simply a device to engage and motivate him.
So to answer OP's specific question, it's neither an "authoritative command" nor a "request" - it's patronising advice (don't say it to your boss at work, for example!).