If there's no field on your layout based on Customers from the Print table (that needs to be filled) then the ID will not be passed to the Print table. Perhaps use a script trigger to create $ID variable and create a new record in the Print table.
And auto-enter calculations will not update to show a new value if the referenced field that was changed is not from the same record as the field with the auto-enter calculation. You might need to use an unstored calculation field with the same expression instead.
I think I resolved my issue with a script trigger that adds a new record to the second table and setting my Record ID in both tables to Get (RecordNumber). This just seemed like there was a "check box" I was missing somewhere or I was setting up the auto entry fields or the ID fields incorrectly.
Regardless, with your responses I was able to understand my problem and create a resolution.