I know from this RStudio Community post 2 that if I click 'Delete' on one of my students' projects, the project will be moved to the student's personal workspace.
The post that you're referencing here is actually talking about deleting a space, not a project. If you click the "Delete" button on one of your students' projects (and confirm in the dialog that pops up), that project will be moved to the space's trash, and if you empty the trash, that project will be deleted permanently. The "Remove" button will do what you expect: send that project to the student's personal workspace.
Related to this: if you remove a user from a space, all projects they have created will be sent to that user's personal workspace, including projects in the trash (those projects will be moved to the user's personal workspace trash). If you don't want this to happen, you'll need to "Delete" the projects in question and then empty the trash before removing space members. In the future, we'll be adding a facility to control what to do with projects authored by a user when removing them from a space.
Also, we're about to release a change that will fold the "Remove" functionality into a broader "Move Project" dialog. I mention this in the event that you open RStudio Cloud in the next few days and wonder where the "Remove" button has gone.
Hope this is helpful, please let us know if you have any questions about this (or anything else).