OP, I've not encountered this problem with my iPhone6 and iOS 9.1, nor have I had any strange issues with calendar items -- I'm running 7.0 on my MS.
I did have some very bizarre issues earlier this week with what ended-up being (summary form): a missed call from the day before that would appear as an incoming call that wouldn't answer, and when I responded to the IC or 17" pop-up, the other would remain -- intermittently as I was driving and every time I'd enter my MS... And loss of most of the media player controls, along with some oddities with Nav routing. When I called Ntl support, he had me delete pairing of my iPhone from MS, then verify it was gone from my iPhone, reboot my iPhone, (I had already rebooted the 17" and IC multiple times), repair the phone with MS, and from then on all has been back to normal. He was suprised, as apparently this sort of thing occurred with prior iOS, maybe when iPhone6 first came out, and prior MS software levels, but not in recent times.
Net of the story... As was suggested, Try unpairing your phone, make sure it's gone from your phone and MS, then re-pair, and see if the problem magically disappears. ...as to if its a MS or Apple problem, well, I'll leave it to others that love to speculate to throw their 2-cents worth in. I reported it to a Tesla and moved on.