Militias were under government control, but it was usually local control, not by the states or the federal government. However that changed with the passing of the Constitution, which provides that Congress, and thus the federal government, has the power "To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;" and "To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;"
It also provides that "The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States;"
Thus governments do control the militia, as a militia, when called up. BUT, the second amendment doesn't protect any right of the states, but as it says "the right of the people".
The so called justification phrase "A well regulated Militia being necessary to the security of a free state" does not allow for restriction of the right protected by the main clause. Such explanations are common in state Constitutions, especially the early ones.
Actually, they would have considered it a select militia, although it doesn't fit their model of such exactly. They are militia because they are not full time soldiers, as the members of the standing army are. The Framers, for the most part, did not think too highly of a select militia either, but for reasons that probably mostly don't apply to the National Guard of today.