I don't think there is a universal rule, for any exercise, about what should be stretched afterwards.
Some dysfunctions may be more common than others (e.g. bench press leading to tight pecs), but ultimately it all depends on what gets tight on you.
Personally, I squat a lot (daily in one way or another, with barbells or kettlebells 3x a week), so I don't feel like the Hindu squat leaves me particularly tight anywhere.
Just listen to your body.