Yes, that's normal. It's because when the HDMI-connected TV is turned "off", it's not really off just on standby, and it fails the HDCP protocol check from the Directv box, and so the Directv box cuts off all outputs. The way to solve this is to get a powered HDMI splitter and connect it between the Directv box and the HDTV, using just one of its outputs. Then the protocol will be supported even when the HDTV is switched off.'
Most good powered HDMI splitters will work. Try monoprice.
If you physically disconnect the HDTV from the Directv box when it is off you will find that works also, but that's really inconvenient