Apparently the Mail program decides when to check for new email messages and how often and when it does this depends on whether the Mac is running on mains power or batteries. It is not clear what this means and even the help file does not make it much clearer. This will probably be set to Automatically, which is the default. On the General tab is Check for new messages. Open the Mail app, go to the Mail menu and select Preferences. What has the battery got to do with it? A lot, as we will see.
It is all to do with the email account settings on the iPhone and the Mac, and to a certain extent, whether your MacBook is plugged in to the mains power supply or is running on the battery.
It will turn up some time later, maybe in 15 minutes, 30 minutes or even longer. Yet when you look in Mail, there is nothing new. You can instantly see who is emailing you and what the message is about. As soon as an email arrives, the iPhone announces it with a chime, turns the screen on and displays the message. I keep my phone on the desk beside me because it is a great way to keep an eye out for anything new.
Have you ever been sat at your Mac and heard the new mail chime from your phone before you get an email in Mail? Why does this happen and what can you do about it?