The reaction attribute of the alien helps mitigate your soldiers' ability to perform reaction fire, as well as their remaining time units. I suspect that sometimes the aliens will intentionally yield some time units at the end of the turn both to allow them to perform reaction fire and to prevent themselves from receiving it. Also, sectoids have a particularly high reaction attribute.
Reaction fire is messed up in the game, with high reaction attributes on aliens causing unrealistic scenarios. You can take advantage of this if you disarm an alien and surround it with pistol-equipped soldiers, to train up their reactions. Once the reaction stat on your soldiers is nice and high, you will find they will react at the slightest provocation. The training will probably also have a wonderful impact on their ability to hit as well.