You do not need an internet connection to run applications, only compiling them for the system using the online compilation service. If you are using Windows to communicate with the modules then you can download the RM1xx firmware from the Laird site, create a folder named 'compilers' in the UwTerminalX folder and put the XComp_*.exe files in that folder, then you can compile applications for that firmware locally on your PC without an internet connection. The RM1xx itself does not require an internet connection.
The code you write (smartBASIC) is running on the BL620 (or BL600 if using the peripheral firmware), the RM1xx has 3 smartBASIC extension manuals on the documentation tab: LoRa functions (the functions you can use for the LoRa module), BLE Peripheral functions (the BLE functions you can use if using the peripheral firmware) and BLE Central functions (the BLE functions you can use if using the central firmware). In addition you can use any of the smartBASIC core functions (listed in another document) in any firmware.
The compilation and download process for RM1xx is the same as BL600, code your program, save it as a .txt or .sb file, open UwTerminalX and setup the connection to your RM1xx board then click connect, right click and select 'XCompile + Load + Run' and select your code - if you have the required XCompiler locally on your Windows system then it will use this to compile the application otherwise it will use the online compilation service - the code will then download to the module and once finished downloading the program will execute. If there is an error then you will get a popup error box describing what the problem is.