>>22595931They happen alongside each other.
In the Kanto Post Game, you find Jasmine talking to Erika about working up the courage to go to Sinnoh and compete in contests.
Jasmine shows up at Sunnyshore in D/P/Pt., and then also in the Pokémon constests.
Then, returning to her gym in HG/SS after beating Kanto, she mentions being in the contests, and will trade you the Steelix she used, Rusty.
>TL;DRBy the time Dawn/Lucas reaches Sunnyshore, Ethan/Lyra have beaten the League and made it to Kanto. By the time you beat D/P/Pt., Ethan/Lyra have headed back to Johto, their journey also complete.
