How do you get the battery light to go off when you replace the alternator in 1999 ford windstar?

I have a 99 Windstar and when my mechanic replaced the alternator the battery light would not go out he took back about 2 alternators, stating that the alternator was not good, because the battery light stayed on. Finally, he had the last one he put in tested and it was fine, but the battery light still came on. He called a Ford mechanic and they said you have to use a ford alternator, because the computer can not recognize other brands of alternators. Once he did the light went out. He said occasionally it will recognize an off brand, but when it doesn't the battery light stays on and it can cause problems with the computer, and I believe he said the cyliniod could burn out. He just bought a re-built alternator from the ford dealer for about $199.00