Ah, so you have to explicitly choose the Exit command after doing the Save command?
Viewing post in Conquest of Helios (Playdate) comments
Oh, I just mean once you choose "Save game" from the menu, you'll see "Current game state saved." come up in a dialogue window. Press A or B, then when you're back at the map again you can do whatever you want at that point, including Home screen to exit the game (or the exit game menu option if you so choose).