I would definitely ask at your next appointment what you should do if something urgent happened after hours- who you would speak to and who would oversee your child's care.
Re your question about how our centers handle emergencies:
At our center, there are multiple drs as part of the cf team as well as a specialized cf nurse. If it's during regular business hours when I call, I usually talk to the nurse, who discusses what's going on with the dr, and she then calls back. Occasionally the dr calls back him/herself, but generally I'm able to get the care I need & feel comfortable with for my dd through the nurse. There is ALWAYS someone on call after hours at night and 24/7 on the weekends, and when the answering service pages them I speak to the dr directly. If Emily needs to be seen, she is sent to the ER at the hospital where the CF center is. It's a longer drive vs. taking her to the local hospital where her pediatrician has privileges, but worth it for them to directly oversee her care and have access to labs, xrays, etc.
eta> If you are asking what the cf center is like in general, ours is located at one of our state's 2 children's hospitals and has a team made up of multiple members: pulmonary drs with a special interest in cf, a nurse w/additional training in cf, a dietitian, respiratory therapists, a clinical research coordinator, physical therapist. The entire 'team' is there on scheduled clinic days a couple days a week; the rest of the week a dr and nurse are always available but you wouldn't be able to get an appt with the whole assembled team.