I recently purchased a AUVIO MHL adapter ( male micro USB to female HDMI) for my Galaxy Tab 4 10.1 (sm-t530nu). It uses a external power supply and also included the Samsung 11 pin adapter. I had read on a website that it does support MHL so I didn't think it would be an issue. However, it did NOT work and I tried with and without the adapter. After some browsing I found a miracast/allshare dongle on amazon for 22$ with free shipping and it works like a charm for the screen mirroring. I did notice while browsing that best buy had a "accessory kit" for the tab 4 10.1 that included a wall/car charger, OTG cable, and a MHL adapter. It was a dongle that plugged into your TV HDMI port and had a USB port that you connected the tab 4s charger to. So maybe it does support it and they just made changes to the connectors pins. It may have just been a mislabeled product also, who knows.
What allshare/miracast device did u buy?