1984 Dodge Omni Antifreeze is leaking onto the passenger fl

The heater core has two tubes sticking out of the heater box and the hoses attach there. I am sure you are aware of this, those tubes are part of the heater core. So if there is no leak at those connections and there is no coolant leftover in the heater box then the core you installed is leaking. It happens all the time. Maybe it was never tested or it cracked during shipment or it cracked installing it. If the fluid leaking in is coolant that is the only thing it could be. Unless it is water that is building up in the box because the little rubber drain on the bottom of the box is blocked or missing. Then the air will blow water back in the car if missing or the water will build up and leak if its stopped up in any way and that is it. Good luck though.