Rates are controlled by each individual property. More accurately, it's the revenue management software that determines which rates are available.
While never at a Hilton, I did work for many years as a Revenue Manager. Rates were set once each year and the computer did the rest. A single rate plan could have multiple rates and the software would select the most applicable rate based on anticipated demand.
I worked at hotels that catered to business-people in a major metropolitan area. Weekends were usually much slower than the week. As an example, our weekend leisure rates could be $79/night in the dead of winter when no events were happening Downtown. Conversely, if there was an NFL game, major concert, or other big event, the same weekend leisure rate could be as high as $209/night. If multiple events were happening and the software believed people would pay more than the highest rate within that weekend leisure rate, it wouldn't be offered and guests would only see "rack" rates.
Due to the complexity of the software, rates are not calculated in real time. Instead, the system will run in batches. Once complete, the results are uploaded to the chain's systems to be distributed to the various booking channels. If necessary, I could re-run the calculations between the scheduled batches. That only happened when an extraordinary event happened (like the airport closing due to weather or the announcement of the dates of major regional event like the NCAA Final Four).
So, to answer your question, there really isn't a set time because it varies based on individual hotel.