The "Offline Mode" option disables a custom map to access the Internet, it works just similar to the iOS's "Mobile Data" setting, that limits the map to download any new map content from the Internet.
Anyway, if you've viewed this map before, those viewed map content are saved as local cache, cache would be reused for next viewing of the same content prior to downloading them again from online servers.
Anyway, caches are designed for performance improvement, not offline viewing. Because cache might be cleared at anytime by the app when necessary.
If you want a specified region of a custom map to be independently viewed offline. It is suggested to use "Custom Offline Map" function, not the "Offline Mode".
You need to download a offline-map by specifying a map, download region and zoom levels, and the app's Download Map feature:
1. You need to start a map downloading with a specified map, region and zoom levels. check this doc for how:
http://duweis.com/support/viewdoc.html? ... =056_dlmap. After that, you can view it without Internet
2. You can also make offline maps with desktop softwares, such as MOBAC, check this:
http://duweis.com/support/viewdoc.html? ... ad&from=mp. Save them as supported format ssuch as .mbtiles. Then upload that file to the app and load &view on the map.