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I think there's a general understanding in the business world that e-mail is for non-urgent stuff. It it's that important and you didn't make the effort to call, that's on you.

When I had a job that provided iPhones I routed all my personal e-mail through the Yahoo mail app and all my work e-mail through the Apple Mail App. Then I shut off notifications for the Apple Mail App so I only got notified about e-mail to my private account.

It depend on the job.
My job require a lot of data with urgent email for discussion. Some of these data in different file format not easily can be clarify on the phone or IM. Email to transfer data is the only way to help each other understand.
 
If you use Gmail then I highly recommend using Google's "Inbox" app. You can create "Bundles" based on queries and then you can choose specifically which bundles send a notification to your Apple Watch.

So you can have a Work bundle that doesn't notify your Watch and another bundle called "Work Mentioned" that WILL notify your Apple Watch if you receive a work email that specifically mentions you or is addressed directly to you (i.e. Not from a mailing list).

It's a bit easier if you use Gmail in a web-browser (on your desktop) to set up complicated auto-labeling... and then choose those labels to be Bundles (and whether or not to receive notifications about them) in Inbox.
 
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