Plex Web allows the server owner to download media files stored on the server. It is separate from Downloads for Offline Use, which is supported for the mobile apps and Plex Desktop.
The error message you mention indicates your mobile devices are connecting via Plex Relay, not via Remote Access. Plex Relay connections are tunneled through servers at plex.tv. They are limited to 2 Mbps (1 Mbps w/o a Plex Pass) and do not support Downloads for Offline Use.
You can monitor streaming via Plex Dashboard → Now Watching + Expanded View. If the connection is Indirect, then it is using Plex Relay.
You should also verify that remote access on your server is configured and functioning correctly. See the Plex Remote Access documentation and The Basics of Remote Access Troubleshooting.