Emails in Apple Watch Notification Center

I chose to send my emails to the Notification Center on my Apple Watch so that the watch doesn’t alert me every time I get an email. Sometimes they haven’t been showing up in the watch Notification Center, just on the phone. The phone is also locked & emails still don’t go to Notification Center. However, they start to appear in the Notification Center after I check the emails in the Email app on the watch. Is checking the emails on the watch a necessary step for the emails to appear in the Notification Center or do I need to do something else?