Why does water come from toilet supply when water to house is shut off?
Unless you have some phantom water supply, the water you are seeing is standing water from pipes higher than the ballcock valve you are trying to change. Is there a hot water mixing valve connected to the cold supply for the toilet? This is common to supply warm water to a toilet to control sweating. If so, is the water heater at a higher level than the toilet valve? If this is the case, try shutting the supply to the mix valve.  With all that said, you may have to simply put a collection vessel under the offending tubing and let the water drain out.  It will stop eventually after all the standing water above it has drained off. If you open the faucets on other fixtures located higher than the toilet, the draining will happen faster.  Of course, an obvious check would be to  assure the main shutoff is completely closed, and not leaking by.