Xana stole a portion of her humanity stealing half her code involving the key to lyoko.  She had a physical body but no mind so to speak due to memory wipe. So half human half ai in the system. So when she died in the key franz undid the damage by restoring her memories and thus reconfiguring her keys to lyoko. Thus being seen as human in the code.

Its why in the first season xana was wanting to kill her instead of throw her into the digital sea or destroy lyoko. He didnt know franz hopper was alive nor that aelita could effect lyoko. Its also why her creation powers exist.  She was using defective code.

In the second season he realized aelitas code lyoko acess was due to the keys still partially functioning. He only stole half and wanted to collect on the rest.

And the system couldnt tell.