A person messages on a Discord server and leaves. Would a reply to their message notify them

@mentioning someone will generate a notification for the person mentioned (They'll get a "you were mentioned on ..." notification)

It will also generate a notification for everyone assigned to the card (They'll get a "someone commented on the card" notification)

Until there are push notifications, folks can set their notification emails setting to "Instantly" at https://trello.com/my/account ... then they should get an email very soon after the @mention or comment.

You may have two logins with your account—e.g. you may have Chrome and IE and have logged into them both at the same time; doesn't matter if one screen is closed because you are logged in online.

If it still doesn't work, I can’t help you but when I started to use Chrome, I had my YouTube on IE still logged in and the inbox notifications wouldn't go away until I looked at them as well as the ones on Chrome. After you do that, log off your leased used browser and that's it. This is just my experience.