When I have my Genie opener "learn" the code for the chamberlain hub, then my wife's cadillac can't open the door. When I have the opener "learn" her cadillac then the chamberlain hub can't open the door.
Sounds like one of two things. Either your genie is only capable of using one remote (this previous one is always wiped) or the learn option on the genie seems to be wipe and learn based. You may want to check the manual for your genie to see it’s capabilities with more than one remote (think of the Chamberlain as nothing more than a remote).
I was able to resolve this after reading other posts. The issue was that the Genie model I have can only store 7 codes and evidently they had all been used by previous vehicles and remotes. To solve it I had to wipe out the memory of the opener and then re-program all my current remotes and devices.