The tutorial progress storage is based on the tutorial's ID. If your tutorial doesn't explicitly set the ID, then a default value is chosen based on a few things. It's possible that something about how the tutorial is run on RStudio Cloud is causing the default identifier to change with each run.
I think that adding the following to the YAML frontmatter of those tutorials this will clear up for your users, even on RStudio Cloud:
tutorial:
id: math350_lrt_1_introR
version: 1 # change the version when you want to invalidate past progress
If not, please feel free to follow up here or with an issue in the learnr repo.