Under DT, and MWI, which are not the same, you wake up in all the universes you were ever in.
ETA
You might have a concern about your measure being dominated by simulations.That isnt the same as jumping. Also, you can only be simulated if you ever had a real life, so it’s possible to take the glass half full view, that the simulations are a bonus to a fully real life, not a dilution.
Under DT, and MWI, which are not the same, you wake up in all the universes you were ever in.
ETA
You might have a concern about your measure being dominated by simulations.That isnt the same as jumping. Also, you can only be simulated if you ever had a real life, so it’s possible to take the glass half full view, that the simulations are a bonus to a fully real life, not a dilution.