1.Mutual consent, meaning logically, approval by Congress or by Convention of the States.
2.Or "...by usurpations or abuses of power justly having that effect," meaning a serious breach of compact rendering its binding obligations null & void.
Did either of those conditions apply in 1861?
No, not even close.
So those declarations of secession were "at pleasure".
I know you don't think that nullifications of the Constitution by various Northern states blocking the return of fugitive slaves were not serious enough to justify secession. Perhaps you are forgetting that the return of fugitive slaves was voted for unanimously by the Constitutional Convention. That and other similar compromises between North and South helped make the Union under the Constitution possible. There was a lot of give and take between the two regions to get to the final Constitution.
According to the description of some of the horse trading at the Constitutional Convention by the authors (Edward J. Larson and Michael P. Winship) of "The Constituional Convention, A Narrative History from the Notes of James Madison":
On August 24, the eleven-member committee reported its recommendations to the Convention concerning the major outstanding issues relating to congressional power over trade. With respect to the slave trade, it recommended a compromise forbidding Congress to ban the importation of slaves until 1800. The following day Charles Cotesworth Pinckney of South Carolina moved that the date be changed to 1808. The Convention approved this motion, with New Jersey, Pennsylvania, Delaware, and Virginia voting no. With respect to statutes regulating international shipping, or "navigation acts," the committee recommended striking the southern-inspired restriction requiring two-thirds majority in each house for their passage, and the Convention passed it on AUGUST 29.
On August 28, as a concession to the South, the Convention unanimously approved a requirement that fugitive slaves in any state "be delivered up to the person justly claiming their service or labor."
As I've posted before, and I'm sure you know, Daniel Webster, who served twice as Secretary of State, and also as a Senator from Massachusetts, and a Representative from Massachusetts and New Hampshire, warned the North as follows in 1851:
If the South were to violate any part of the Constitution intentionally and systematically, and persist in so doing, year after year, and no remedy could be had, would the North be any longer bound by the rest of it? And if the North were deliberately, habitually, and of fixed purpose to disregard one part of it, would the South be bound any longer to observe its other obligations? I have not hesitated to say, and I repeat, that if the Northern States refuse, willfully and deliberately, to carry into effect that part of the Constitution which respects the restoration of fugitive slaves, and Congress provide no remedy, the South would no longer be bound to observe the compact. A bargain cannot be broken on one side and still bind the other side.
And yet, some Northern states continued after this warning to flout the Constitution. To save bandwidth, I'll link to one of my earlier long posts citing reports of what some Northern states were doing: Link
Of course, it's not my opinion on this which matters.
What matters is that Southerners themselves did not think such things necessarily cause for secession prior to the election of Lincoln in November 1860.
So long as Washington DC remained in friendly Democrat hands, Southerners were content to let politics play its course.
Only with Lincoln's election did they suddenly decide that every grievance, no matter how minor, was now just-cause to declare secession.
In reality, those were not "reasons for secession", they were just convenient excuses.
The real reason was to protect their "peculiar institution" against "Ape" Lincoln and his "Black Republicans".
Finally, on the issue of Northern "nullification", seems to me the Compromise of 1850 should have rendered them mute anyway.