No idea about the timing.. But I do know this day in age, these kids almost always have their next move lined up when they leave. Parents, old coaches, handlers, etc. take care of all of that before hand.
I agree with Birdman, it's a real sorry move in regards to his teammates. Ultimately he has a job, though not the job he wanted, and if Hurts was to get injured the season would be on his shoulders. Not like starting QB's don't go down... Especially a running QB like Jalen. When you consider that he literally cannot play anywhere this season and that year of eligibility is lost, he gains nothing by leaving now. I'm normally on the side of the kid transferring but in this case its hard to justify.