Overall you may have Cursor installed on more than one machine, however the same account should be used on one machine at a time. You do not need to log out but avoid running multiple instances on different machines.
Hey, you can use a single account on multiple computers (2-3 devices is fine), but avoid using it simultaneously. Running the same account concurrently on multiple devices may be flagged as misuse by the system. As long as you access your account from one device at a time, there shouldn’t be any issues.