But on CX 888 you are not "connecting" to another flight into the US, rather just continuing on the same flight, so the advice is correct. If you were connecting to AA then you would follow the instructions. The only exception would be if connecting from a JL flight to CX888!

A few years ago now, but the time I took CX 888 we were just herded into a holding pen before reboarding a little while later, no re-screening, but also no pre-clearance of immigration. Of course taking CX 889 last year (JFK->YVR->HKG), no such issues and we were asked to stay on the plane.