Okay, I checked.
If I right click on fire mode, it becomes orange, and saving of TUs for overwatch works.
But I still would say that this is a bug.
There is a button on top of fire modes which says "overwatch". It is clear and obvious (100x more obvious than right clicking on the modes), but apparently this button doesn't work, though I expected it did. You can left click on "overwatch" button and it will switch to "overwatch off". When it says "overwatch off", I would expect a soldier not to save TUs for overwatch. But if the fire mode is 'orange', then soldiers do save TUs for overwatch even though the overwatch button clearly says "overwatch off".
This is extremely confusing.
My suggestion on how to fix it: remove right click / orange color thing. If "Overwatch" button is on, save TUs for overwatch; if "Overwatch" button is "off", don't save TUs for overwatch.