I have an M3 Perfect MiniSD and what you have described sounds like you have the "AutoSave" option in the M3 settings set to "No". With this set to "No" you don't get the screen at the start up for the save file backup as you mentioned. Also if you play a different game to Mario your Mario save file will be replaced by the new game and your Mario save is lost forever. The "AutoSave" option needs to be "Yes" for saving to work properly. After Which you will see this screen at start up (Apologies for the image quality).Im not sure how the saving works, but for example, i am able to save in game in mario and the next time i start up the cardtridge theres no sign of any save file being written unlike ez flash where it will show a loading screen for the save file. I can then start up mario and my save will be there.
Best console experience for me is the Game Boy Micro. When combined with the M3, the greater portability makes it my favourite even against my backlight modded AGB-001.