Actually, the time banking was my idea. (I don’t really want credit or anything, just clearing it up.) But I’m not sure how it applies under your system.
Do actions in your system take any amount of real time? Or, if I have 24 TUs, can I instantly move 24 squares? If it’s the latter case, the TUs already are a form of the time banking. Essentially, while you are away from the computer, TUs are accumulating in the bank, and then you expend them when you get back, instantly.
So if I log in at 1:00, and have 8TUs on a unit, I move it 8squares, and log out. I come back at 11:00, and have 10TUs ready to spend. The time from completing the last action to logging in again is saved as TUs.
That’s different than Travian, where each action takes some amount of real time. In that situation, it looks more like this:
I log in at 1:00, and move a unit 8 squares, and log out. It takes 8 hours for the unit to move to that position, and it gets there at 9:00. I come back at 11:00, and have wasted 2 hours. The time from completing the last action to logging in again is lost. If the time bank were added to this system, those 2 hours would be sitting on the unit (call them TUs if you like) and I could immediately move the unit 2 more squares.
So in brief, if I’m understanding TU’s right, they are the same as my “time bank” except you’ve put a cap on them at 24 hours.
Now, you’ve mitigated the obsessive login issue a bit, but not completely. For example:
What if I have a resource harvester unit in my home base, and a resource mine of some sort 6 squares away from home base. Assume the harvester can carry one chunk of resources, which is enough resource to build 1 unit. At midnight Monday, the harvester has 0 TU. At Noon, it has 12TU, at midnight Tuesday, it will have 24TU.
Player A logs in at midnight Tuesday, spends 24TU on two round trips to the mine, and gets 2 resource chunks. He spends those resources one two more harvesters, for a total of 3 harvesters, with 0TU each.
Player B logs in at noon Monday, spends 12TU on a round trip to the mine, gets 1 resource chunk, and uses it to build another harvester. At midnight Tuesday, each harvester has 12TU. He sends both of them to the mine, getting 2 resource chunks. Then makes 2 new harvesters. Total: 4 harvesters with 0TU each.
Clearly player B gets ahead.
I can think of only one way off the top of my head to mitigate the issue even more, and it’s awfully hairy and confusing: Each unit could keep its own clock, and know exactly when it is in time. And when you log in, you can take actions that bring all your units up to the present time, in whatever order you like. Sort of a revisionist history of “what I would’ve done if I were logged in.”
In this scenario, Player A above logs in at midnight tuesday, sees 1 harvester with 24TU whose clock says “midnight monday.” He spends 12TU on a round trip to the mine, which sets the unit’s clock to “noon monday,” and leaves it with 12TU He gets 1 resource chunk at his base marked “noon monday”, and uses it to build another harvester. The new harvester’s clock is also marked “noon monday,” which gives it an immediate 12TU to spend. He sends both harvesters to the mine, getting 2 resource chunks, spending all their TU, and setting their clocks to the present, midnight Tuesday. Then he makes 2 new harvesters. Total: 4 harvesters with 0TU each, all marked with the present time. Just like he would’ve had if he logged in at noon like B did.
With all his units in the present, A can log off and go to sleep happy. 
This would likely be a real pain to implement, but I’d play it.