How are item rewards in the crucible rewarded?

Randomly is correct. I have had wins where not a single person on my team got an item, and I have had losses where Strange Coins were handed out.

RNG(Random Number Generator) is the ultimate decider on who gets what.

But it does seem to favor those who rank lower to encourage them to stick around. If players who lost and did badly only got further insulted by not getting any items out of it.. they would probably not enjoy playing anymore.

Here are some pictures of end-game rewards that seem to prove this point of it favoring lower ranks

one, an engram is better than blues, even if it's green

two, Legendary engram for bottom rank, top rank did get something, though

three, only bottom ranks got something

four, Legendary for bottom rank again

five, one item, legendary, last place

six, legendary for bottom, blues for top

now, this is a very small sample and I can't say if it's definitive, and without information from Bungie we can't know for sure. That being said, this is a pretty good indication (there is tons and tons more pictures of results screen like this) that the RNG gods favor the weak. In my experience with Crucible, I've never seen a Legendary Engram go to top 3, only bottom 3.