A key element in Patron are families. Individual citizens in the game can be (usually are, but don't have to be) a member of a family. A single family occupies an entire house. This means that while there could be empty rooms in a house, that doesn't automatically mean new immigrants have a place to live. You'll likely have to provide that for them, either by building new houses or by building shelters.
This is quite a big difference to what players are accustomed to in city builders, but this design choice / feature has a clear and logical spot in the big picture of social dynamics and classes. Two citizens can choose to have children. Usually this means three key prerequisites have been met:
- They are at least content with their life in the city
- They have a house of their own
- They have empty rooms in their house
Notice the third prerequisite. This means that the larger the house, the more children your citizens will/can have.
Another thing to keep in mind are social classes. Children, when born, don't start off on the Peasant level. Classes are not experience levels. The children actually start off one class below their parents. Through proper education (another social issue, especially of interest to the Merchant and the Gentry classes), the children can reach their parents' class before reaching adulthood. If they don't, they'll likely have a chance to go up in class during their work. Though the latter depends on what work they find/get assigned to.
As expected, when a family member dies, from whatever reason, the family will grieve. This all plays a role in the happiness of the citizens and their views on different social issues.
New families are created naturally, when two citizens get married. How the individuals got to your city is of no consequence. They could be immigrants, freed slaves, or could very well have been born and raised in the city.