Giordano reported Robyn Missing within 1 hour and 48 minutes after she was last seen alive, he filed a missing persons report with Aruban Authorities, he contacted the American Embassy, Robyn's family was notified.
It seems all the important authorities and people were informed by or via Giordano, I do not see the ticket agent as someone that truly needed to be filled in about the situation. What was he to say to her, that his travel companion had disappeared while out at sea, that they were snorkeling, that he wasn't sure if she would be found alive since a couple of days had passed already? How would the ticket agent react to that, Robyn's flight had not been cancelled apparently since why else would she ask Giordano about his travel companion, so maybe she would ask if he had informed authorities and he then would say he had, but maybe she would think this being a situation where she had to report to her superiors, maybe ALE would be called and he would not be allowed to leave until the superior of the ticket agent knew the proper authorities were aware of the situation.
Giordano wanted to leave Aruba, he was told he was free to leave and had an attorney prior to leaving, his flight was to leave soon, by filling in the ticket agent he would cause commotion with as a result that he probably would not be on his flight. He may have taken his decision not to tell her based on that.
The fact that he wanted to leave Aruba so soon is another discussion, but when just talking about the ticket and me personally still not convinced that Giordano harmed Robyn, I do not see him not willing to share everything that had happened as something suspicious or an outright lie but more as him trying to prevent a situation he did not want to be in.
It would have been different had Giordano caused Robyn to disappear, did not tell a soul, then fled the island and then told the ticket agent that Robyn would be taking a later flight. IMO