I'm sure I fully understand the bug you're reporting. There is no logic in the game that changes your save mode from Free Save to Checkpoint. "Turn back the hands of time" resets you back to the "Volt" Character screen and overwrites the slot as intended, so you can't click restart and then reset-that-restart. Is that the "auto save point" you mean?
Please join the discord if you'd like to describe your issue better: https://discord.gg/cPSGacUX3X
Edit: Bug resolved, user's browser was failing to properly recognize subsequent save files. Switching browsers resolved the issue. Likely a localStorage issue (or perhaps related to third-party cookies for itch.io). Direct download-and-play would make the file work too I'm guessing.