If an airline adds a new route or changes its flight times, does my website pick that up on its own or do I have to update it myself?

Yes, it picks that up on its own. The flight results on your portal are not a stored list that somebody has to keep current. Each time a customer searches, the request goes out to the airline or the supplier at that moment and comes back with the routes, times and seats being sold right then. So when an airline opens a new route or moves a departure time, it shows in your search results without you doing anything, and there is nothing for you or your staff to load in.

Where it works differently is a booking that has already been made. If an airline changes the time of a flight your customer is already holding a ticket for, that does not come through a search, it arrives separately as a schedule change notice from the airline. Whether that notice reaches you on its own, as an alert inside your portal or as an email, or whether someone on your side has to go and look for it, depends on the supplier the booking was made through. Some pass these on properly, some pass them on slowly, and some do not pass them on at all.

There is one more limit worth knowing, because it is easy to mix up. A whole new airline appearing is not the same thing as a new route on an airline you already sell. If the airline is one your current supplier does not carry, it will not simply turn up, and adding it usually means another connection has to be switched on, which depends on your plan and on what that supplier offers.

The thing to check next is how schedule changes on live bookings actually reach you, since that is the part that catches agents out rather than the search side. Ask your supplier where those notices land and make sure someone on your team is watching that place every day.