Peel and cut the potatoes into 2-inch chunks. Add to a pot with water and season with salt. Bring to a boil. Cook until tender. Drain and run through a potato mill or ricer into a large bowl.
Add the remaining filling ingredients and mix to combine. The amount of paprika isn't listed, you just want enough to get a good color. Taste and adjust seasonings as needed, adding some more pickle juice or mayo if it is too stiff.
Put the mixture into a piping bag.
Preheat the oven to 25 or 50 degrees higher than the instructions on the package of tots says. Put the tots on a pan and drizzle with oil and a sprinkle of salt. Toss the tots on the pan to coat. Spread them apart and cook until crispy and browned, as long as it says on the package, flipping them once during cooking, about ¾ of the way through.
Plate the tots, then pipe the potato mixture onto each tot.
Add a piece of pickle to the top of each, then sprinkle with paprika and chives. Serve.