ROTFLMAO.
The state of New Jersey originally voted to ratify the 14th, but when its representatives observed the methods that its proponents were using to coerce the Southern states into ratification, NJ rescinded its ratification (to no avail).
Of course to no avail. Once a state votes to ratify an amendment then that's it, the Constitution does not contain any provisions for revoking ratification. The reasoning should be obvious - what if a state legislature voted years later to revoke ratification?
Hence, the U.S. Congress considered the southern states as having never left the Union only until such time as it became politically expedient to declare that that they had.
I was not aware that the New Jersey legislature had the power to declare a state out of the Union.
Excuse me, but I don't think you read it very carefully. New Jersey didn't declare a state out of the Union. New Jersey clearly recognized the statehood of the 11 states. New Jersey was complaining because the federal congress withdrew recognition, for the singular purpose of eliminating opposition to the 14th amendment, after more than a quarter of the existing 37 states rejected it.
(Actually, IIRR, Congress declared these 11 states to be "non-states." As a precondition for re-entering the Union, these "non-states" had to ratify the 14th, yet Congress neglected to explain how a "non-state" could legally ratify a constitutional amendment.)