Phantom/induced current. With the wires disconnected on both ends, they get an induced current from nearby wires. With the wires connected to the panel, the neutral (white) is pulled to ground, and I suspect that helps keep the hot wire "less hot". Either way, the current you are seeing is likely extremely low. Instead of a non-contact tester (which is always a good safety check), use a multimeter directly on the wires and I expect you will not see any real voltage.

Phantom/induced current. With the wires disconnected on both ends, they get an induced current from nearby wires. With the wires connected to the panel, the neutral (white) is pulled to ground, and I suspect that helps keep the hot wire "less hot". Either way, the current you are seeing is likely extremely low. Instead of a non-contact tester (which is always a good safety check), use a multimeter directly on the wires and I expect you will not see any real voltage.