I know it seems to be a difficult concept for many to grasp, but Lincoln did not call out militia to oppose secession, regardless of how lawful or unlawful secession itself may have been.
Lincoln called out militia to suppress insurrection, rebellion and acts of war committed by secessionists against United States military property and officials.
These acts of war against the United States began simultaneously with, or even before, official declarations of secession.
They culminated in the Confederacy's formal declaration of war against the United States, on May 6, 1861.
However, my point is that secession by a whole state at the behest of a large majority of its people is not the same thing as the "insurrection" described by Congress in the Militia Act. I find it extremely unlikely that the 1790s Congress intended their Act to apply to secession.
Thus Lincoln took an existing law and stretched it well beyond the intent of those who had written the law.
Which is not to say that I believe secession was either constitutional or prudent.
All I am saying is that Lincoln stretched the law well beyond its original intent, as he did in other areas, notably by the constitutionally dodgy nature of the admission of WV as a state.
The problem here is that by definition the Constitution and the legal system are not and cannot be designed to function in time of civil war. Lincoln did his best, I think, to respect the laws while still waging effective war. But he was very often forced into breaking the letter of the law in order to uphold its spirit. And of course sometimes he made mistakes.
BTW, you are quite correct about the timing of acts of war. Numerous southern states launched attacks on US military and other installations well before they had "legally" seceded. Notably VA, which started its troops on the march against Harpers Ferry before the convention had even voted for secession. They did not "officially" secede till the referendum in late May, by which time they'd been waging war for over six weeks.