If you plan to use some of the more advanced dependency types along with 0-day tasks in your project schedules, there are a few things to keep in mind to understand how the scheduling module in CoConstruct will interpret certain values.
If you have a 0-day task that has a Finish-to-Finish predecessor, the task's finish date will fall on the next work day, rather than sharing the same finish date as the predecessor.
On the flip side, if the predecessor is the 0-day task, the task's finish date will be the day before the predecessor's finish date.
If you need to make sure your 0-day tasks and FF predecessors have an identical finish date, you can add lag or lead time to the predecessor to adjust for the finish date.