I’m convinced that something changed in the last few months on Todoist’s end. I’m almost sure that tasks with date/time didn’t used to show the little alarm clock, even when created natively. However, they would still ping a notification if you had the appropriate configuration in settings.
It was the case that alarm clocks would only appear against tasks which you had manually set an extra reminder for i.e., as a prompt some time ahead of the due date.
Incidentally, around November time, Todoist added another criteria for setting a reminder. It used to be either ‘at x date, y time’ or location. You can now also opt for ‘x timeframe before task due date’ if there is a date/time already set for the task. This was just a stealth change; no real mention of it anywhere.