I have a 2003 Kia Sorento. I put a new thermostat in it but it still blows the antifreeze back through the reservoir and out the overflow. The is no antifreeze in the motor oil.

Check the coolant level.

Power Steering Leak Fix 2003 2009 Kia Sorento 2003 Kia Sorento EX 3 5L V6

see if this helps

You'll have to jack up the front of the car, or safer yet, park the car facing up a large hill, and run the car with the overflow cap off while shaking it back and forth. It will take 5-10 minutes but you will get a lot of air out, after this add coolant and drive around, you heater should work better. This may have to be done multiple times to completely purge the system of air.

Yes, it should. Heat expansion pushes coolant through the hose into the reservoir. When coolant cools, it will siphon back into the radiator until radiator is full.

You will want to taste the leak (or get someone else to do so) and make sure it is not water.
Antifreeze has a very sweet taste.
You should only need one drop, and be sure to rinse your mouth out really well afterwards.
Whenever a radiator is replaced, the hoses attached to it can also begin to leak, because the rubber hardens with age, and can be harder to seal again.
I prefer a stainless steel band clamp, not the original equipment.
A good flashlight would be a help as you look for the problem.
Be sure to check the heater hoses, and the other hoses that carry coolant, as any of them could be leaking, due to "being disturbed" or due to the possible higher pressure the new radiator is giving the cooling system.
Be blessed.

Heater coil

Is the engine temperature normal when driving or is it on the high side? After a short run turn engine off and check coolant hoses, be careful they may be hot to touch, squeeze the top hose, if it is very hard, you may find the coolant pressure is too high causing the coolant to leak from overflow, this could be caused by faulty thermostat, head gasket or poor coolant circulation, also check cooling fan is operating when hot

you shoud not have to change it.this wouldbe long life
antifreeze have the PH check at a shop

If the cap is not ontop of the Radiator itself it means you have a remote reservoir. Usually its near your washer fluid filler but not always. On the side of that are a full and fill lines simply check them for a level and add fluid as needed there.