There is no standard method of sending (pushing) a message to all devices attached to a Wi-Fi network. If there was a way, it would be easy to find the specification and point to how it is to be done. Unfortunately, it is difficult to prove the absence of something.
As you clearly realized, it would be possible to do so if an appropriate page which you control was open in a browser, or application running, on their device. You could develop a framework where users have to sign on and keep a page open, or application running, in order to connect to your Wi-Fi.
Given that you control the router, it would be physically possible for you to write code which intercepted the packets being transmitted through the router and inserted such a warning within the HTTP of pages being sent to the various connected devices. This assumes that they are using HTTP to view normal pages. You could, of course, also insert a warning in other protocols. Depending on your jurisdiction this might be illegal, or have other legal issues. I would consider doing so to be a Bad Idea?.
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