Sometimes when unplugging my iPhone 6s from the charger, the screen stays black without waking up. I have checked and determined that did charge the battery so I know it had a good connection. If I get a phone call (while plugged in or after unplugging) sometimes I can hear the ring tone but the screen is still black and I cannot see to swipe the answer button. I have to hit the home button to make the screen come alive. This happens intermittently and only while plugged in or just after. Anyone else have this experience?
I don't think that I've ever gotten a call on my iPhone 6s while it was charging before, but I can say that some of the little things about the iPhone 6s are buggy, like how some system sounds don't always play.
All that I could recommend is to update to iOS 9.1, as my iPhone 6s is noticeably less buggy on 9.1 than it was on any earlier iOS 9 release.