I am able to mirror the Samsung Galaxy Tab SM-T520's screen to my TV over an HDMI cable. I see the screen on both devices. But as soon as I start a video, the tablet screen goes to an image of the traffic cone and a symbol indicating it's playing the video externally. If using the built-in player, the video also disappears and shows an indication of the fact that it's sending video externally. In both cases, various playback functions are available on the tablet, just no video is displayed there.
So rather than mirroring, it's sending the video to either the tablet or the TV, but not both. This only happens with videos; the rest of the apps show in both.
I have poked around at the (very few) settings in the various players, but so far have not found anything that will allow video to show both places. The tablet is on Android 4.4.2. Is there any kind of OS trick to get the video to play on both devices?