If the iPhone is near to iWatch, the iWatch will start sending the files to iPhone automatically OR you can also check by clicking on the Plus icon on the shelf, which shows the 'Import From Apple Watch' option (attached screenshot). While receiving at iPhone side, if the iCloud is enabled on the iPhone (as suggested here - http://support.noteshelf.net/knowledge-base/how-to-enable-icloud-sync-in-noteshelf/), the files will then be transferred to iCloud so that other devices configured with same iCloud account will receive them and show up in the UI.
Please take note of the following & try the suggestions to fix the issue -
-The iCloud needs to be enabled on your iPhone and iPad (if you want the recordings to also show up on iPad)
-And both these devices should be using the same Apple ID/iCloud accounts. You can make sure of this via the ‘Settings’ app of your iPhone/iPad devices
-Restart Apple Watch as this usually fixes such issues
-Please use “Send To iPhone” option when long pressed on recordings screen in the Watch. Note: File transfer time depends on audio duration
-If the sync is still not working automatically, uninstall it from the Apple Watch and install again from the new Apple store of the Apple Watch, restart the app on iPhone (provided any of your new data on the watch is already backed up onto the app on iPhone/iPad to avoid data loss).
If issues persist, pls send us the logs via Gear icon->Support->Contact US->Send Logs from your iPhone to which the apple watch is configured so that we can look into the flow and suggest accordingly. Thank you.