From what I remember researching on my own and reading here in the forums, it's imperative to contact them in advance... and then again at intervals leading up to the flights to confirm.
I believe there are folks that have done flight changes/diff legs as you will be so they can prob provide guidance here but my assumption (and I think it's a safe one) is that you will need to contact BOTH airlines to arrange this.
Personally, I wouldn't risk it by waiting, I'd contact them asap just to be sure there aren't any kinks, and if there are, you'll still have time to resolve.