I thought of the saying "it takes one to know one". Genie saw through Anastasia's story from the very beginning. In fact, she may have even decided to take on Anastasia after the manager told her she was now an orphan from the plane crash. Considering Genie knew everyone on board, she would have known Anastasia was lying from the get go.
Once you tell a lie, it is hard to remove yourself from the new reality you created. In Anastasia's case, the parties kept getting bigger, the clothes better, and the cash allowance grander. Anastasia thought of herself as an actress awaiting discovery and rationalized her very first lie with the thought that SHE was going to comfort Genie during her time of loss. The fact that Genie knew from the beginning proved that Anastasia was not as good as she thought she was. She was embarrassed for being "caught". She had a narcissist personality. Everything was supposed to be about her. But Genie one upped her!