I have a S4 and the notifications did not work until I deselected a third party texting app as the default messaging app on the phone. Now that it is no longer the default messaging app, the notifications are working.
It worked fine on most devices before release. Sometimes an update will cause an issue. I have the S7 edge and it worked perfectly. Was able to get texts and everything on watch and reply. Now I no longer get text alerts on the watch. Nothing changed but an update. At any rate, hopefully they fix it soon