2000 SLS severe overheating w/new radiator install. Put original back and it's fine.

Original radiator in my 2000 Seville has a small leak where the pin on the top of the right radiator tank broke off. Bought a new radiator off ebay, installed it and filled it with coolant (via the overflow tank, of course). Ran it at idle until the thermostat opened and put more in until it was full. Drove it and within about a mile or so it got warmer than usual so I turned around and by the time I got home the temp gauge was past 2 o'clock with the "engine hot" warning flashing. Parked it for a while hoping the cooling down process would help with purging and added more coolant and drove it again with the same result. I removed the new radiator and put the original back in and after the refill with a heat up and cool down and another top off it ran normal (needle at 12 o'clock). I ran water from my hose into the new radiator's openings and it came out the opposite one seemingly just fine. I should point out in was a very inexpensive part (about $70 shipped) from a company called Sunbelt Radiators (Here's the link: https://www.ebay.com/itm/Radiator-For-Cadillac-Seville-4-6-2279/261430991368?ssPageName=STRK%3AMEBIDX%3AIT&_trksid=p2057872.m2749.l2649), but if the water flows through it shouldn't that be what really matters as far as just the cooling aspect? The car has over 185,000 miles so I don't want to spend any more than is necessary since it's a pretty tired looking and driving vehicle and a second car. I checked local yards for a used one but all they have are post-2000 models which aren't compatible. Any ideas, advice, or suggestions? Anyone buy one of these radiators?