Will the flight price my customer sees in the search results still be the same when they come to pay?

Not always, and that is normal in flight selling. Fares come live from the airline at the moment of the search, and the cheapest seats on any flight are being sold all over the world at the same time. Between the moment your customer searches and the moment they reach the payment page, those seats can be taken by someone else, the airline can reprice the fare, or the taxes can be worked out again. A flight booking API checks the fare once more just before the ticket is issued, and that final check is the one that counts.

A well set up portal deals with this by revalidating the fare before payment and telling the customer plainly if it has moved, so they can accept the new amount or go back and pick another option. How that message looks, and whether the customer sees it before or after they choose the flight, depends on how your portal is configured. Holding search results for a short while makes searching feel faster but makes a price change more likely, while going back to the airline every single time is slower and steadier. Your supplier and your plan decide how much of this you can adjust.

The difference is usually small, and it can move down as well as up. What you want to avoid is collecting the money first and finding the change afterwards, because then you are left choosing between absorbing the difference yourself or going back to a customer who thought the booking was done.

Ask your supplier how your portal revalidates the fare before payment and exactly what your customer is shown when the price moves, and get into the habit of telling customers that a quote holds only for that moment rather than for the rest of the day.