When the connection between the iPhone and the Apple Watch are not successful or you have not paired with new devices you may see a "Start Round on iPhone" message on your Apple Watch even after starting a round on your iPhone. This means the signal from your phone is not reaching your Apple Watch.
This can be resolved by repairing your devices.
This process takes a few minutes, so make sure you can set aside that time and keep your Apple Watch connected to the charger. https://support.apple.com/en-us/HT204568