How long is start date? 00h00mm00ss or a 24hour period?
After testing, here is how it works.

If we use again my example with twice the same event date 3rd of April:

Status 1: from membership date to start date
Status 2: from start date to end date.

Status 1 will change by the end of the 3rd of April which means start date from the previous status is "Master" and start date lasts 24 hours. Status 2 will appear on the 4th of April. And this is not related to cron Job.

So if you want to start Status 2 on the 3rd of April at 00h00'00", for example if an Insurance is running from this date or if the member has to be of legal age, then set the end event of Status 1 on start date and -1 Day.