The same way things of this nature are always handled: a few lines of throwaway expo.
They're going to need more then a few lines, especially for Ezra. I'm not one to say people generally need a lot of information to understand something like this, but Rebels isn't something that the general Star Wars audience has any real knowledge of, and it seems like Ashoka is going to require a lot of knowledge of it to make sense, probably way too much knowledge. The Mandalorian was an original character, Boba Fett was a known character and kind of similar to Mando and every Star Wars fan knows Obi-Wan. Even Andor at least comes from a movie that was generally well received and most current SW fans probably watched.
But Ashoka, to most people that have watched the movies and watched the live action shows, is a side character from Mando (remember, most people that watch Mando probably haven't even seen TCW), and Ezra is a character from a cartoon that had less of an audience then TCW and he has a more convoluted story. The show is going to have a bigger need to explain things to the general audience then any of the other shows did, and honestly I think it was a poor idea to tie in Rebels to it at all, which goes back to Ashoka's live action introduction in Mando. People like my Dad aren't going to bother going to a wiki to read up on the characters/cartoons, they need the information in the show.
Its things like this that make me wish Filoni had no influence over the live action stuff. I don't think he knows (or cares) that the general audience that makes SW movies and the live action shows successful generally don't watch any of the cartoons, so making a whole show dependent on knowing stuff from the less popular SW cartoon seems like a bad idea to me. Its fine to reference them and bring characters in where appropriate, but tbhis isn't just having Cad Bane show up in a spot that could be any bounty hunter, this is a show trying to follow up on the stupid Time Travel non-finale of Rebels.