Seems the onten adapter has those types of issues. Amazon.com: Onten Lightning to HDMI Adapter, 1080P 8 Pin Lightning to Hdmi Female Video Adapter with Lightning Charging … Varying reviews on Amazon for it.
Many third party connectors lack the HDCP support required to correctly mirror the iPhone to the TV, and have issues like that.
Best bet is to use a certified Digital AV Adapter from Apple.