Yeah /tmp is shared by everyone. It's just how Plesk servers work (I know some other products put a user's /tmp inside the home folder which IMO would make more sense, but it is what it is). You shouldn't be able to save things anywhere besides /tmp and ~ though, and there are certain commands, files, and folders that can trigger a permanent ban if their account is seen messing with them.
In fact, people tend to fill up /tmp accidentally quite a bit with broken Node apps (passenger logs get saved there, and when people do things like write bad apps, or delete their node app without turning node off, passenger sits there slowly filling /tmp with logs until the server breaks). You'll get suspended for filling /tmp, and monitoring to automatically handle /tmp filling up is a project currently on our radar since its a common issue. We had an outage on Morty due to a full /tmp the other day.
As for the space limit not changing in Plesk, consumed disk space is only recalculated a few times a day, so you can technically exceed the limit up front, but it will automatically suspend you when the next recalc happens.