I just tried auto-wrangling some critters and the animation before the wrangle was from grooming, not from wrangling. Here is the situation afterwards when the critter is already wrangled.
Maybe this happened because the grooming station was right next to the critter drop off?
1. get some critters in a stable.2. Set auto wrangle below the critter limit, so some critter gets wrangled. 3. When wrangling, the grooming animation is displayed instead of the wrangle animation.