A couple iMessages have gone to Apple Watch but not the paired iPhone

I have had this happen exactly twice in the last few days, each occasion being with a different contact. I’ll receive a text message and feel a tap on my wrist. The message comes in to the watch, but never arrives on the phone.

My Apple Watch isn’t even an LTE model. How is this possible? I do not have (or want) iMessage in iCloud enabled.

But this new behavior is troubling. What should I do? Thanks!

Update: Before I could even post this message, I just happened to see that the message from the first occurrence (Saturday) arrived, completely without fanfare, still bearing the original timestamp and marked as an unread message. This is very strange. Dare I hope the other message (first sent to me within the hour) will eventually be delivered to the phone?

The message that just arrived was the latest in its thread, while I have sent and received other messages in the thread that still has an outstanding message. I have no idea if that will be a factor in the future delivery (or nondelivery) of the missing message.

Versions:
Watch OS 7.3.3
iOS 14.4.2

I turned handoff off and disabled iMessage on my computer and my iPads to keep the messages from coming to those devices. On the Watch app on the phone, under messges make sure that mirror my iPhone is not checked. That should help.

I’m confused - what does “Mirror my iPhone” do? Mine is checked and sometimes a message shows up on both devices, sometimes it doesn’t. Petulant Apple devices?!

I’m not sure, either. I only use iMessage on my phone and my watch. It’s not even set up on my Mac, and I don’t use iCloud in any capacity, so I don’t think Handoff is a factor.

I would assume that one would want Mirror my iPhone to be enabled. At least, it seems logical.

It’s a setting for how notifications arrive on the watch. watchOS is designed to allow notifications for almost all apps on either the watch or the phone but not both. If the phone is being actively used (the display is on and the phone is unlocked), notifications go to the phone, and otherwise they go to the watch. By turning off mirror my iPhone for message notifications you can have custom settings on the watch for how many times you get notified of a message if it remains unread, whether read receipts get sent for iMessages when you read the message, or whether notifications arrive on the watch at all (in that case, they will sound and/or vibrate only on the phone.) It doesn’t affect whether the messages actually get delivered to the watch.