Steps to reproduce

1. Set up a repeat, always active command block that teleports a wither to the same location on every tick.
2. A short distance away, set up a bedrock platform and a repeat, always active command block that teleports other mobs to the center of the platform.
3. (Optional) set up a repeat, always active command block to summon particles for tracking the path of wither skulls: /execute @e[type = wither_skull] ~~~ particle minecraft:villager_happy ~~~
4. Set up a group of impulse command blocks that in quick succession (a) destroy items, (b) summon a new mob, and (c) damage the mob so that it has only 1 health remaining.
5. Use the impulse command block group to summon mobs one at at time. With each mob, observe what items drops when the mob is killed kill, whether the dying mob gives off wither effect particles, and how those results relate to the trajectory and impact point of the wither skulls.

Expected results

Wither roses drop from all mobs killed by wither shots.

Observed results

Wither roses do not drop when mobs with 1 health are killed by direct hits from a wither shot. Wither roses only drop when the skulls explode near the mobs that they kill but do not hit them directly. In the case of direct hits, the mobs give off wither effect particles just before dying. This indicates that they are taking fatal damage from the wither effect (which does not trigger a wither rose drop by design MC-138109) before the explosion damage is factored.