Julia Lynch was arguably the child of "transient" aliens, and she was found by Vice Chancellor to be a United States citizen. A New York State law, at some point prior to 1860 or so, said:
The specifics of the case are immaterial to the point. The New York Legislature passed a law in violation of the Premise upon which Lynch v Clarke was based. The Court said English Common law applied, the Legislature said "no it didn't."
So according to New York law, the children of RESIDENT aliens, born in that State, were born CITIZENS of that State.
I've said repeatedly that there's a case to be made that children of tourist aliens are, or should not be, not natural born citizens of the United States.
Now you are starting to get it. Slaves were permanent residents without citizenship. Wong Kim Ark's parents made their home here but could not become citizens because of the Treaty the US had with China.
So the law you refer to shows that the State of New York never required citizen parents, as long as the parents were simply resident, in order for a child born there to be a citizen of the State.
Permanently resident. An immigrant, more or less.
Different states had different requirements. Some were easier than others. They had control over whom would be a citizen of their own states, but the status of being a "natural citizen" of the United States (i.e. Federal citizen) was not subject to state laws. (except in terms of who was grandfathered in.) It was based on Natural law, as was our own independence. The argument for US Independence was completely contrary to common law, or the Law of England. It's only basis for legitimacy was "natural law". Under Common law it was forbidden.
States generally tended to adopt the English common law, and then change whatever parts of it they liked.
“The laws of the United States fall under three classifications: treaties made under the authority of the United States, the law of nations,(Vattel), and the Constitution and statutes of the United States.” John Jay