If an airline changes the flight time on a booking I have already made, does the system tell my customer or does my staff have to spot it?
In most cases the system can pick it up and tell both you and your customer, but how reliable that is depends on how the airline or supplier sends the change to you. A schedule change is not something the booking system can work out on its own, so it only knows about it if the change arrives as a message it can read rather than as a plain email to someone's inbox.
Where your flights sit with a GDS or an airline connection that pushes change notices, those notices land against the booking automatically. The system can mark the file as changed, show the old and new times side by side, put it in a queue for whoever owns that customer, and send the traveller an email or a message letting them know before they turn up at the airport. For corporate accounts you can also let the travel desk or the arranger see the same alert so they are not hearing it from the traveller first.
The honest limit is that not every supplier behaves this way. Some consolidators, small carriers and bed bank style suppliers only email a human, and in those cases nothing reaches the system and your staff still have to read the inbox and update the booking by hand. Even when the alert does come through, actually accepting the new time, moving the traveller to a different flight or asking for a refund usually needs a person, because what the airline allows differs from one fare to the next.
The sensible next step is to list the suppliers you book most and ask each one how they send schedule changes, then decide which changes should go straight to the customer automatically and which should stop in a staff queue first.
