Zotero Standalone 5
Standalone 5.0 is installed correctly for all users on both profiles. However, a current problem I see when switching between profiles is that when I am logged in to Zotero in user1, I am logged into the same Zotero account when I am logged into my workstation as user2 and the same is true when I am logged out; it seems like Zotero 5 does not allow for multiple profiles. Obviously a problem for public workstations.
Also, Zotero doesn't really have the concept of "logged in" (except for the forums/website of course)-- there is sync and there's the local database. I'm not sure which of the two you're referring to.