What is the fault code? I have purchased junk keys from part stores before. If it is the
key you should have a "key code invalid" fault.

  Is the part new? Used? If it's new, I only see the tumbler assembled sold WITHOUT transponder keys. If it's used, I would try the process again, you might be using the incorrect function, I would do a parameter reset as well besides erasing all keys. I personally think that you purchased the one that comes with keys that DO NOT have transponders. I have seen a few people do this but not realize the keys they got with the new tumbler have no Transponder Chips. Let us now. 

Just reset the parameter after you program the key

Do a parameter reset

That don't supprise me. I don't buy keys from part stores anymore. They caused me
too much greif in the past.

 I only buy trusted aftermarket keys. Ford uses Strattec which is the company that manufactures their keys. I went to a Ford dealer and purchased 40 bit keys for a 2005 explorer. He handed me Strattec keys, lol. After that, I only buy this brand and it has never failed me. They also sell 80 bit and the new 120 bit. They are cheaper online than the dealer. 

 From back when I programmed a few Mazda cars, the original tool would as me for input or output code. Not sure if the autel bypasses that? But once I did that, I was able to program and erase all keys. Not sure how the autel works, have never done one yet and it's been years since I have seen a mazda. Goo luck!