If another airline issues the ticket for travel on CX (including award bookings), CX will usually refer you to that airline for any changes not caused by them. For instance, you want to change your dates before departure, you miss your flight because you woke up late, etc.

But for misconnections, CX doesn't care which airline issued the ticket when it comes to rebooking you. They'll still put you on the next available flight and provide you with a hotel room and meals (if applicable).

In short, you'll be fine. Nothing to worry about