Not always, and it depends on the supplier and the type of rate. Some hotel rates are fully flexible and the price can shift up or down based on availability and demand, even after your customer has seen it on your portal. Other rates are fixed and locked in once your customer searches, so the price they see is the price they will pay. The hotel API will tell you which type of rate you are looking at, but you need to make sure your portal is clear with your customers about whether prices can change. Some portals show a note that says the price is only guaranteed once they complete the booking and payment goes through, while others hold the price for a short time after search.
When your customer moves forward to payment, that is usually when the price is confirmed and locked by the hotel supplier. At that moment, if the rate has changed, most systems will either tell you the new price or pull the booking back and ask your customer to search again. The exact behavior depends on how the API is set up and what rules you have configured on your portal.
You should check with your portal provider about how price changes are handled in your setup, and whether you want to show your customers a message that explains when prices are guaranteed. You should also look at the rate types coming through from the hotel suppliers so you know which ones are flexible and which ones are fixed.