Traveled to the nether and was hunting blazes with bow and arrow, after killing several, noticed that none were dropping blaze rods or xp orbs. I afterwards switched to creative and tested a few different scenarios... I found that killing mobs in the nether with melee will yield xp orbs/ loot. Killing nether mobs in overworld with arrow or melee will also yield xp and drops. In the overworld, I teleported over a 1000 blocks away and killed a few things with bow and arrow and that also seemed to give xp and drops. Did not matter if shot from crossbow or bow.

So, just seems that arrow kills in the nether do not register as player killed mobs.

steps to recreate.:

1 go to nether

2 kill a mob with bow and arrow

3 No xp or player killing drops