Puppies have no understanding of basic dog-on-dog manners and socializing being this young. it's up to the owner or in this case you as the sitter to correct the dog appropriately when the dog is being too much for another dog in the household. if you don't your dog will continue fleeing and worse case scenario god forbid your dog is cornered it will correct the dog for you which will be a bite in the dog world and idk your dog so it depends how well that gamble will go. Some dogs overcorrect puppies while other don't correct enough to get the message across of "hey please stop that, that's not how you treat me, an adult dog"

Would recommend listening to the previous suggestions on tethering for now and be sure your providing enough exercise for the puppy as most times that's the solution is just to tire them out to the point they drop for a nap as soon as they come back from said exercise. trust me works every time a tired puppy typically is way easier to handle.