The Roman Census never required people to travel to their homeland. That would be quite counterproductive as the practical purpose of census-taking was the calculation of taxes, which requires an enumeration of property.
The bible's account of Roman census' is seemingly not accurate.
Usual explanation is that doing census by place of birth was actually Jewish idea - because the "12 tribes of Israel" concept is so deeply ingrained in their culture, so whey Romans requested census Jewish leaders simply tried to kill two birds with one stone, and Romans didn't really care so they agreed.
The bible's account of Roman census' is seemingly not accurate.
https://en.wikipedia.org/wiki/Census_of_Quirinius