I have had experience with doing what you are doing And, the black magic mixer you are using.
1. The Broadcast standard for television is either 1920 x 1080 x60i OR 1280 x 720 x 60p. It never defined an output for 30p.
The Sony NX5U is set to give you one or the other of those outputs, which at that time seemed to be the most compatible with broadcast TV. And still is, by the way.
You can see that right in the menu of the camera, in the output section, it says vertical 1080i or 720p.
2. The Black Magic is a great little mixer for the price. HOWEVER, everything has to be the same, inputs, and probably outputs too. It is not like the more expensive ones, that can frame convert on in real time.
3. When I had a similar problem, trying to sync the output to a switcher which was also had an input from a computer, I found the following worked.
a. I set up the NX5u for downconvert the output in squeeze mode(4x3)
b. Then we connected the sdi cable to the mixer.
c. We told the mixer the signal was really wide screen aspect ratio, and it made it 16x9.
The net result was that the mixer was happy, people could see the live video and the computer, even though it was not full high definition. But I was recording in 1920 x 1080.
I suspect the same thing for you. The streaming world is full of lies. They call high definition to sizes and bit rates which are less than high definition. If you truly tried to send it at full high definition, it would be choppy and blocky to 90% of the recipients.