When setting a due date, what is the time zone for which you are setting it? Is it possible for each user to have their own time zone so that when a team member in one zone sets a deadline the correct date/time is reflected for all other users on the team?
Trello stores the due dates in UTC, however it displays (and interprets) due dates in your local timezone (i.e. whatever your OS/Browser are set to), so the due date will be correct for your entire team, no matter what time zone they're in.
Here's an example of how this would work:
Suppose you are in New York, and you set the Due Date for the "Finish the slides for the presentation" card to 4:00 PM EDT, so they'll be ready for a 4:00 PM meeting.
New York is using EDT (UTC-4), so Trello will interpret (and store) that 4:00PM as 8:00 PM UTC.
8:00 PM UTC - 4 hours = 4:00 PM EDT)
If the person responsible for finishing the slides is in California, which is using PDT (UTC-7) then when Trello displays the card for them, the due date will appear as 1:00 PM PDT.
8:00 PM UTC - 7 hours = 1:00 PM PDT)
If they finish the slides at 12:55PM PDT (5 minutes before the deadline) and email them to you, and it takes the email 1 minute to arrive in your inbox, you'll see it arrive at 3:56 PM EDT, just in time!