The damage increase should show up in your sheet damage as long as you are moving. Since hydra and sentry damage is based on your own damage, it should apply to them as well.
I know of people who use Hexing Pants of Mr.Yan on their Witch Doctors with pet builds and it works great.
Tested just now (don't have the pants, I took my weapon off, cast hydra, put the weapon back on) - the damage of hydra is calculated at the moment of cast and doesn't change when your damage changes unless you recast, so you will have to be moving when you cast hydra, but you don't have to keep moving once it's summoned.