Following the below procedure should make sure you are always working in the SP document itself (and you don't have to do a manual save)

• 1) open the document in the desktop app (Excel or Word) - open in browser is also possible, but it does not give the same functionality)

• 2) Have a look at the top of the document (saying "AutoSave On") and make sure there is no "saved to your PC" after the filename.

• 3) You also should be able to see the other users editing the document at the same time (if there are any) on the right side of the screen.