Hey there, DesertRatR.
After reviewing your post, it appears that the email account you use on your iMac and iPhone XR isn't syncing correctly with your iPhone. The only way to make sure the accounts are showing the same messages is to restart your phone, and we’re glad to help with this.
First, go to Settings > Passwords & Accounts. Select the correct email account, then "Delete Account" at the bottom. Once the account is deleted, restart your iPhone.
When your iPhone is back to the Home screen, use the steps in this article to add it back again and see if the actions you take on your Mac appear on your phone: Add an email account to your iPhone, iPad, or iPod touch
Let us know how that goes.
Take care.