How does Appian determine which Task to show after an AND Node?

With the process chained to both nodes, you would be creating a race condition and there would not be a guarantee of the tasks displaying in any particular order. It sounds like you want User Input Task (UIT) A to be chained, and UIT B available once UIT A is complete and available as a Task in case a user decides to complete UIT B before A on their own.

One solution could be to chain to UIT A and not to UIT B. Create a UIT C that is identical to UIT B and chain it after UIT A is complete. You can also chain UIT B to UIT A assuming UIT A has not been complete. Add logic to automatically cancel whichever UITs have not been opened by this user to avoid creating duplicate tasks.

With the process chained to both nodes, you would be creating a race condition and there would not be a guarantee of the tasks displaying in any particular order. It sounds like you want User Input Task (UIT) A to be chained, and UIT B available once UIT A is complete and available as a Task in case a user decides to complete UIT B before A on their own.

One solution could be to chain to UIT A and not to UIT B. Create a UIT C that is identical to UIT B and chain it after UIT A is complete. You can also chain UIT B to UIT A assuming UIT A has not been complete. Add logic to automatically cancel whichever UITs have not been opened by this user to avoid creating duplicate tasks.