A Gettysburg victory for the CSA or a Peace Democrat win in 1864 (Atlanta not fallen) are reasonable PODs for a CSA victory. At this point you have a significant number of slaves who are behind Union lines, and if it begins to look like the CSA will gain independence, any and all slaves/contrabands who can will try and get as far north as possible, certainly north of the states that will go to the CSA.
A scenario where the CSA is in a position to demand the return of any contrabands/escaped slaves from the USA is ASB in my opinion. Once the border is in place, escape from the CSA will be very difficult unless the slave is very close to the border. How welcoming the north is to slaves will be an interesting question, some may see the blacks as the cause of the CW and the severing of the Union. Others will be sympathetic.
In an independent CSA, with borders much more tightly controlled than the slave/free line before the war, escape will be very difficult. Internal controls on slaves will be much tighter than before the war, with the contraband experience proving to the masters that, contrary to their opinions, their slaves were not happy with their lot, "lovin de old massa". Also, whatever restraint the owners practiced in the south due to pressure/opinion from the north is out the window.