Resizing a model or a part changes the PivotPoint in-game?

I'm assuming you're using my answer from the previous question. Sadly, you can't change model's pivot offset. However, if you want to get the original pivot, you can create the attributes OriginalPosition, OriginalXDirection, OriginalYDirection, and OriginalZDirection in the model since a pivot (aka CFrame) has a position and a direction. To get the CFrame from position and direction, use CFrame.fromMatrix(position, xDirection, yDirection, zDirection).

function ScaleModel(model: Model, xScale: number, yScale: number, zScale: number): Model
	local cf, _ = model:GetBoundingBox()
	local origin = cf.Position
	
	local OriginalPosition = model:GetAttribute("OriginalPosition")
	if OriginalPosition == nil then
		model:GetAttribute("OriginalPosition", origin)
		OriginalPosition = model:GetAttribute("OriginalPosition")
	end
	local OriginalXDirection = model:GetAttribute("OriginalXDirection")
	if OriginalXDirection == nil then
		model:GetAttribute("OriginalXDirection", cf.XVector)
		OriginalXDirection = model:GetAttribute("OriginalXDirection")
	end
	local OriginalYDirection = model:GetAttribute("OriginalYDirection")
	if OriginalYDirection == nil then
		model:GetAttribute("OriginalYDirection", cf.YVector)
		OriginalYDirection = model:GetAttribute("OriginalYDirection")
	end
	local OriginalZDirection = model:GetAttribute("OriginalZDirection")
	if OriginalZDirection == nil then
		model:GetAttribute("OriginalZDirection", cf.ZVector)
		OriginalZDirection = model:GetAttribute("OriginalZDirection")
	end
	
	local originalCFrame = CFrame.fromMatrix(OriginalPosition, OriginalXDirection, OriginalYDirection, OriginalZDirection)

	local scale = Vector3.new(xScale, yScale, zScale)
	
	for _, obj in pairs(model:GetDescendants()) do
		local OriginalSize = obj:GetAttribute("OriginalSize")
		if OriginalSize == nil then
			if obj:IsA("BasePart") then
				obj:GetAttribute("OriginalSize", obj.Size)
			elseif obj:IsA("JointInstance") then
				obj:GetAttribute("OriginalSize", Vector.zero)
			elseif obj:IsA("SpecialMesh") then
				obj:GetAttribute("OriginalSize", obj.Scale)
			end
			OriginalSize = obj:GetAttribute("OriginalSize")
		end
		
		local DontScale = obj:GetAttribute("DontScale")
		if DontScale == nil then
			if obj:IsA("BasePart") or obj:IsA("SpecialMesh") then
				obj:SetAttribute("DontScale", false)
				DontScale = obj:GetAttribute("DontScale")
			elseif obj:IsA("JointInstance") then
				DontScale = false
			else
				DontScale = true
			end
		end
		
		if DontScale == false then
			if obj:IsA("BasePart") then
				local newSize = OriginalSize * scale
				obj.Size = newSize
				
				local distance = (obj.Position - origin)
				local rotation = (obj.CFrame - obj.Position)
				obj.CFrame = (CFrame.new(origin + distance*scale) * rotation)
			elseif obj:IsA("JointInstance") then
				local c0NewPos = obj.C0.p*scale
				local c0RotX, c0RotY, c0RotZ = obj.C0:ToEulerAnglesXYZ()
				
				local c1NewPos = obj.C1.p*scale
				local c1RotX, c1RotY, c1RotZ = obj.C1:ToEulerAnglesXYZ()
				
				obj.C0 = CFrame.new(c0NewPos)*CFrame.Angles(c0RotX, c0RotY, c0RotZ)
				obj.C1 = CFrame.new(c1NewPos)*CFrame.Angles(c1RotX, c1RotY, c1RotZ)
			elseif obj:IsA("SpecialMesh") then
				local newScale = OriginalSize * scale
				obj.Scale = newScale
			end
		end
	end
	return model
end