Exactly how are you entering the first time before autofilling? I've tried it in the way that you describe in your first post and everything is working the way that I said it should, with no dates shown.
The exception being if you autofill more than 96 rows (using 15 minute intervals). When it goes from 23:45 to 00:00, that is actually 24:00 or 1 day, not 00:00. The increments continue, it does not reset and loop back to the beginning, meaning that it will go to 24:15, 24:30, etc. If this is what you are encountering then you need to stop filling at 23:45 then copy the fist set of times and paste down instead of filling.
Also note that if you are using an alternative application then it may work differently. What I have described is based on excel. Alternatives like google sheets, open office calc, or anything else may not be the same.