Thanks for the reply -- my apps are independent Watch apps (Watch only) not related to an iPhone app, so the Automatic App Install setting doesn't have any effect on them. The one that does is in the Watch app under "App Store", but unfortunately this seems to be turned off by default and nobody thinks to look there.
I am glad to know that there is an alert directing customers to do a manual install if automatic install does not start, but it seems like customers are not paying attention to that or maybe they do not know what to do or to look on the App Store on the Watch itself. In fact, based on the contacts I get from customers, they do not understand the concept of independent Watch apps and they don't even know there is an App Store on the Watch. Three years ago I could understand this, since independent apps were new in watchOS 6, but I would have hoped customers would catch on by now.