For reports or processes that allow you to use the relative date T, TA translates that to the current system date. However, if it is between midnight and 6 am, TA will subtract 1 day from it to treat it as the day before. So running a report for transactions today at 2 am using start and end date T will be treated as date T-1, so run on yesterday. Similarly, if you run it for yesterday with T-1, it would then become T-2.
This will also apply to TA processes where you use a relative date. Like if you run Update Current Start Date on the first of the month at 2 am, telling it to set the current start date to T-1M (today's date minus 1 month), at that moment it will be treating it as the day before, which would be the last day of the previous month in this situation. So run at 2 am on 5/1, it would be treating T as 4/30 instead.
The solution is to either run the report or process after 6 am, or modify the date parameter appropriately to account for the fact the T is being treated at T-1 at that point (so for it to actually count as today, use T+1).