When you setup either an LCS Wifi module or the similar DCS WIU or the new WTIU there are 2 possible modes of operation.
Access Point= standalone network with NO internet VS Join to Network= device is connected to an existing wireless network likely also with internet
One mode, the device acts as a client and connects to your existing wifi network. You then also connect your tablet or phone to your home wireless network, and in theory, because both devices are on the same network your phone can talk across your wireless network to the LCS module and ALSO, because you are connected to your home network that has internet connected to it- the phone or tablet STILL HAS INTERNET. Again, in this scenario- your tablet or phone is connected to your home or office wireless network that ALSO has internet, and just so happens- you programmed the LCS or DCS wireless module to ALSO connect to that same home network.
OR
If you setup your device in a standalone network, where the LCS or DCS module is standing up it's own access point with a wireless SSID (example Lionel LCS-850B) that network is completely isolated. Literally, your phone or tablet is talking directly to that LCS Wifi box, and you cannot plug an internet cable into your LCS Wifi Module- so that network (Lionel LCS-850B) does not have internet.
And yes, now many phone or tablet operating system may tell the user this. The message means nothing (regarding you operating LCS or DCS) if you knowingly connect to an isolated network specific to the module (again, network named LCS or DCS is a huge clue).