AA does automatically upgrade people on the waitlist when space opens up, but it's not instantaneous (most likely, the upgrades are done through a separate batch process that runs periodically). It's been long reported on this forum that you can call in and "jump the queue," so to speak, if you find availability through EF or otherwise.

ETA: I just realized this was a ticket purchase, not an upgrade situation. In that case you might not have been waitlisted for J on the shorter segment, so you would indeed need to call in. (I was in a similar situation with an award ticket last month, one leg in economy and the other in F, and just had to keep an eye on availability for the former).