Yes, revenue management software do account on reservations accessed through third party also. Especially you are talking about Citi’s fourth night free offer, where revenue management software can restrict availability of discount or availability of other offer such as fourth night free. Such is done on airline award availability, also. For example if United has an award seat available on its United flight. That does not mean United’s partner airline Lufthansa has access to the same award seat on that particular United flight.

Hilton can sure limit and control the availability of fourth night free offer by Citi. That can be nothing to do with revenue management, the condition of under what circumstances forth night free offer is valid and what circumstances fourth night free offer is not valid (such as your case of 3 night + 2 nights separate reservation) can be already written in the contract between Hilton and Citi regarding fourth night free offer.