You assume correctly. Multi-round & the unlimited tourneys work the same .... if you start as a Pro, you will be considered a Pro for the hole tourney.
Back in the good old days, that would pose a problem because clubs were tier-specific. If you advanced to Master, you unlocked/bought longer(better) clubs to use from the longer tees. But you couldn't use those "master" clubs in subsequent rounds because you started s a Pro.