Will a customer who booked on my website be able to see that same booking in my mobile app?

Yes, as long as the app and the website are working off the same booking system and the traveller signs in with the same email or phone number they used when they booked. The booking is not stored in the app itself, it sits in your system, so the app simply asks for it and shows it. That means a booking made on a laptop in the morning can be opened in the app the same afternoon, with the same reference, the same passenger names and the same voucher.

The part that trips people up is guest bookings. If you let customers book without creating an account, there is nothing tying that booking to a person the app can recognise. Most systems solve this by letting the traveller sign in later with the same email and pull the booking in, or by sending a link in the confirmation email that opens the booking directly. It is worth deciding which of those you want before the app is built, because it changes how the sign in screen behaves.

How much detail the app can show also depends on the supplier. Your own reference, the dates, the passengers and the voucher will always be there because they are yours. Live updates from the airline or the hotel, such as a schedule change or a room upgrade, only appear if that supplier sends them back through the connection, and not every supplier does.

Before you launch, make a test booking on the website as a normal customer would, then open the app and check that it appears with everything a traveller would actually need on the day of travel.