They never became independent though
Well it depends on whatever argument the Union authorities needed to put forth at any given time. When they needed to be treated like "rebel states", they were treated as though they had never left. When they needed to be treated as a "foreign state" they treated them as if they had actually become a foreign state.
As I've said numerous times, the condition of their independence exists in a state of quantum super postion being both "in" and "out" of the Union at the same time, depending upon the legal argument needed by the Federal authorities at any given time.
For example. The Constitution required the federal authority to return slaves to people for whom their labor was due according to the laws of any state.
Lincoln suspended that, which he had no authority to do if they were still states of the Union. Therefore for the purpose of doing that, they were "out" of the Union.
To justify sending an army to invade them, they were "in" the Union.
So like I said, whether they were in or out depends on what Washington DC needed to claim at any given time.