In OS Ticket, I have an email setup for SMTP and IMAP. That default email address is set to retrieve email every 5 minutes, 10 emails per fetch. My presumption is that you don't need to be logged in to the platform retrieve the email. Yet, I don't have any updates until after I've logged in and then the OS Ticket updates all new tickets all at once. So, fo instance, I don't login over the weekend. I get two new tickets, one on Saturday, one on Sunday. I log in, wait, and then they both show up, time stamped for the date/time I logged in. Not great behavior....
Email autocheck?
It sounds like you haven't setup a scheduler and are running auto-cron.
See Schedule Polling
https://docs.osticket.com/en/latest/Getting%20Started/POP3-IMAP%20Settings.html