If an airline changes my customer's flight timing after I have booked, will I find out through the system?

Yes, in most cases you will be told, but how fast the notice reaches you and how much detail it carries depends on the airline and on the supplier the ticket was issued through.

When an airline moves a departure time, cancels a leg or changes an aircraft, it sends a notice back to wherever the ticket was issued. Where your flight supplier passes that notice on through the API, the system records it against the booking so your staff can see the booking has changed when they open it, and it can be set up to alert your office so nobody has to go looking. Some airlines, and quite a lot of the low cost ones, prefer to write straight to the contact details sitting on the ticket instead of sending anything back through the API, so whoever you put in that field is the person who hears first.

Be aware of the limits. Very small timing shifts are often not flagged at all, while cancellations and big changes almost always come through. Acting on the change is a separate matter from being told about it, because accepting a new timing, asking for a different flight or claiming a refund usually has to go back to the airline or the supplier under their own rules, and only some of them allow that to be done straight from the booking screen.

The sensible next step is to ask us which of your flight suppliers return schedule changes through the API, decide whether your office or your customer should be the contact on the ticket, and keep your staff in the habit of reviewing departures a few days out so nothing is missed.