If I leave the refill hose in the Overflow tube it keeps running. But if I just put the refill hose in the tank it fills to the place I have it set at and stops. Is this a problem. The guy at Home Depot says yes but he told me to just replace the toilet. Really I said. It is not the trap because why would it fill at all if it was that. I think it is something in the overflow tube. But do I have to change it.
If the refill hose is placed into the overflow tube (as opposed to clipped above it, as it should be), it could cause a siphon issue resulting in a continuous lowering of the tank water level.
This would normally cause the toilet fill valve to cycle on intermittently (to fill the tank when the level drops low enough to actuate the fill valve float mechanism), as opposed to continuously (you wrote "keeps running"). However, the "running" noise you are hearing might be the sound of the siphoning process itself. video explanation
This phenomenon is well known and can happen with most any fill valve (I won't say all because I just don't know). Your fill valve should have been equipped with a clip or tube guide to hold the refill hose above the overflow tube or to hold it just inside but not lower than the tank water level.
Sounds like the line to the tank fill is plugged and the tank is not getting water flow, time to clean the valve or replace just the valve since it works with the tube in the tank. Turn the water off remove the top of the valve put a cup over the top of the valve. Turn the water on let it flush the valve and turn off. Put the top of the valve back on turn water on and see if the tank fills, if it fills problem solved if it still won't fill the tank replace the valve, flowmaster valves are less than 20$ at most big box stores and very easy to swap out.