Thanks, Joe; it sure is!
I thought I'd cracked it by turning it off and then either/both force-quitting Reminders on my iPhone or/and restarting the device.
Not at all. The only way I can get iOS 9.0.1 (and actually 9 before that) Reminders to synch is by replicating the same change in iOS as I made on either of my two iMacs (which both synch perfectly.
I've also tried posting in the Apple Support Forums but for some reason get the dreaded read banner when I try to submit.