Yes, the federal government gets to make the rule, but nowhere does it get the authority to grant citizenship.
Citizenship was an issue 'among the several States', so the general government got to make the rules of naturalization in order for all the States to grant citizenship to any inhabitants in a uniform manner.
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BTW- You snipped out the most explanatory part:
Federalist #42
There is a confusion of language here, which is remarkable. Why the terms free inhabitants are used in one part of the article, free citizens in another, and people in another; or what was meant by superadding to "all privileges and immunities of free citizens," "all the privileges of trade and commerce," cannot easily be determined. It seems to be a construction scarcely avoidable, however, that those who come under the denomination of free inhabitants of a State, although not citizens of such State, are entitled, in every other State, to all the privileges of free citizens of the latter; that is, to greater privileges than they may be entitled to in their own State: so that it may be in the power of a particular State, or rather every State is laid under a necessity, not only to confer the rights of citizenship in other States upon any whom it may admit to such rights within itself, but upon any whom it may allow to become inhabitants within its jurisdiction. But were an exposition of the term "inhabitants" to be admitted which would confine the stipulated privileges to citizens alone, the difficulty is diminished only, not removed.
And how does an inability to make the rule as to citizenship leave the power to grant citizenship in state hands? It makes no sense. If the state can't make any rule concerning citizenship, what authority does it have in that area beyond the merely administrative? The first naturalization act, from 1790, stated, "...any alien, being a free white person, who shall have resided within the limits and under the jurisdiction of the United States for the term of two years, may be admitted to become a citizen thereof, on application to any common law court of record, in any one of the States wherein he shall have resided for the term of one year at least..."
BTW- You snipped out the most explanatory part:
And this aids your argument how? It's a "parade of horribles" that illustrates the messy situation of states being given the leeway to determine who shall or shall not be allowed citizenship on their own.