If it helps, Nancy, William Barclay’s commentary on Luke quotes a Roman document describing the same or a similar census:

It is necessary to compel all those, who for any cause whatsoever are residing outside their own districts to return to their own homes, that they may both carry out the regular order of the census, and may also diligently attend the cultivation of their allotments.

John Gill observes that while simple collection of taxes would not require everyone to be present at a specified location, the census which prepared the tax rolls did, and Jesus’ birth in Bethlehem rather than his childhood home of Nazareth was thus a matter of prophetic fulfillment