Exactly ...Even Android TVs open the previously viewed source by default. Some manufacturers modify the OS to open home page on restart. I have checked multiple TVs and behavior is same.
Same way Mi has modified the OS for some reason which is why it opens the home screen. You know Mi has custom launcher (Patchwall), so that can be the reason. Sony has stock Android OS launcher which doesn't opens the home screen on restart. It directly goes to the set top box source if you have viewed it last time.
I was also mentioning what I have seen in my Lloyd TV..
Yes maybe difference in different brands..