"Everyone jump!" is an imperative sentence, which takes the bare form of the verb. "Everyone jumps!" is also technically grammatical but far less likely to be used in practice (as I would interpret it as being a statement of fact, that every person, at some point in their life, has jumped or will jump).
The verb form for imperative sentences is easier to see in this other example:
Be quiet!
It's important to note that imperative sentences don't have subjects. The word that looks like a subject (everyone in your sentence) is actually a vocative, which is basically a word used to get someone's attention so they know you're talking to them. (It's often recommended that it have a comma to offset it.) In fact it is possible to move the vocative to the end of the sentence with no change in meaning:
Jump, everyone!
Another reason we know that vocatives aren't the subject is because they can be used in sentences that already have subjects:
Everyone, you need to come with me.
Vocatives will usually be someone's name or their title (ma'am, dad, professor). You can also use the pronoun you (though that's perhaps a bit rude) or another second person pronoun (which you may come across in various dialects). It's also possible to use a phrase like "whoever took my sandwich".