Spectator Messaging with connected phone does not work during workout

When my phone is connected (i.e., using my phone's connection instead of LTE), I do not receive any spectator messages during my workouts. When the workout is complete and I sync in Garmin Connect on my phone, and then select a new activity, I suddenly get all the messages that were sent during the prior workout. My best guess is it's related to Garmin Connect not actually pushing messages to my watch during the activity, and instead sending it when I sync the completed workout.

This problem only occurs when the watch is connected to the phone (I.e., messaging over LTE works fine). Until this is resolved I’ll have to keep my watch disconnected from my phone during workouts.