They come before the fall of Winterfell by Theon. Like, hella days before. They come as wards to Winterfell by their father, Howland Reed. (whos my homeboy. Hes yet to actually appear in the series but, he ♥♥♥♥in' rules. The book yer reading explains why hes awesome.)

What Jojen is, is a greenseer. Thats a bit different than a warg. Wargs are people who can control wolves/animals. Some call them skinchangers in the story. Because they can usually control other types of animals. Greenseers are peeps who have wonky psychic dreams. They claim its the Old Gods giving them the greendreams. (some remnant of power left over from the Children of the Forest. Bran's arc in the books explains this a lot better.)

As for what makes Bran a warg/seer, im pretty sure the fall awakened that, but after he got visited by the Three Eyed Crow. Remember, in the show, thats what Bran really wants to find. He wants to find that Three Eyed Crow and find out wtf is really going on there. Jojen and Meera encourage this because Jojen had a greendream about it or some cray ♥♥♥♥. lol!

There are things littered all throughout Ned's chapters that really hint to something...interesting. I didnt get it on my initial read but i did on rereads and was all "omfg..." I wont say anything until you finish the book though. In fact, it may be a better idea to discuss it after you finish the series thus far. Mostly because of other little hints littered throughout the other books. (like a story Meera tells Bran once...)
But youre a clever little smelly so who knows....?

Ummm...Did you pay very close attention to his thoughts on Jon...and his sister Lyanna?