Is the hotel price my customer sees in the search results always the price they will pay at the payment page?

No, not always, and it is worth understanding why before a customer asks you about it. Hotel rates and availability change constantly at the supplier end, and the price shown in a list of search results is a snapshot taken at the moment that search ran. By the time your customer has read the reviews, picked a room and reached the payment page, that snapshot can be several minutes old, and the supplier may have moved the rate or sold the last room at it.

This is why a properly built portal checks the rate again before it takes any money. That second check goes back to the supplier, confirms the room is still there at the price quoted, and either carries the customer straight through or tells them the rate has changed. It is not a fault in the booking engine, it is the step that stops you confirming a room you cannot actually deliver.

How often this happens depends a great deal on the supplier and on the market you are selling. Busy city dates and last minute stays move the most. Some suppliers hold a quoted rate for a short window, others make no such promise at all, so what you see is their behaviour rather than something that can be fixed from your side.

If it is coming up often, keep a note of which supplier and which dates it happens on, and take that to the supplier concerned before assuming the portal is at fault.