You need to logout/login 2 times for custom lang strings to be applied

In web, login as admin and go to Site administration > Mobile app > Mobile features. Open the app in a device and login in the site. In web, modify some string using "Custom language strings". E.g. you can use "mm.sidemenu.appsettings" to change the text of "App settings" in the More tab, or "core.sitehome.sitehome" to change the text "Site Home" of the top tabs in the user dahboard. In the app, logout and login again in the site. Check that the texts are updated to match the new strings.