Definitely not normal behavior. I've had them connected previously to my phone, my two iPads and my MacBook Pro, and never once have the AirPods connected while sitting in the charging case.
I would try factory resetting them (I think by holding the case's rear button for an extended period of time, but better check), remove the bluetooth pairing from all your devices, reboot your devices, and re-pair the AirPods to your phone.
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If you only put one AirPod in, the iPhone/iPad will automatically switch to mono and play single channel audio. It will also automatically switch to that unit's microphone for calls.
Put two in your ears, and it will switch to stereo audio and use which ever one (left or right) you've specified in system settings for the microphone.