It’s probably better to avoid it if you can, but it should help to clear the temp files (all of them, not just cookies) before you open the site and after you’ve logged off the site. I would recommend everything but the browser history in private. If you’re in a public setting, just clear it all. That should help, but I do know Fiverr uses IP addresses for “things.” Not sure exactly how they fit into the security though.
If they put a lot of weight on the IP address that would be bad, but if that was the case my speculation is that people at schools wouldn’t have an account very long. I would hope the security is more sophisticated than that.Also, many systems aggregate IPs anyway, but I also know that automated security can get weird.
If you’re using a public computer, it’s definitely not the best (could have something like a keylogger installed).
Sorry I couldn’t give a more definitive answer. Basically try to be vigilant no matter where you’re accessing the site. Security is always important. And try to avoid accessing it where a lot of people are already on it, if you can.
Oh, and always, always uncheck that “stay logged in” box.
You could try asking CS, but I’m not sure you’d get anyone who knows how that part works (or would be willing to tell you, for security reasons).