I'm wondering if I need to let RCL know about it in advance. Has anyone ever left a cruise early and if so, does it cause a problem with customs or anything?
Yes, the cruise line needs to know about this since, depending on the itinerary, it may be against the law and fines could be levied. Specifically, leaving a cruise early could violate the Passenger Services Act. Please read this link
carefully. Is the agent who set up the flight also the one who booked the cruise? I am amazed they didn't tell you about this.