Mac Mail can’t connect from multiple devices on same network

I’ve just added mail accounts to a new iMac (2017 High Sierra), all working correctly. However when I have mail open on the iMac, I can’t log in to the same mail account on either my MacBook Air or iPhone on the same wifi network. If I turn off WiFi and connect through the cell network on iPhone all mail is accessible and properly synced. Same thing if I just close mail on the iMac, then either the phone or laptop can log in fine. What am I missing? I need to leave the desktop mail open in my home office and sometimes work from another room on phone or MacBook. Why do they “block” each other? PS - these are IMAP accounts and it all worked fine on PC desktop running Outlook.