Educating players about what the saving indicator is for, can be done in multiple ways. Starting a new game is a good time to do this, or as a useful hint shown on a loading screen.
An animation is very helpful when it comes to saving indicators. Spinning or pulsing icons can help make the player feel like something is happening.
Some games don’t allow the player to save the game as and when they like. For this type of game, save indicators play a huge role in informing the player that their game is being saved, but they also reassure the player too.