Defining equilibrium position vs equilbrium constant
You're using the word "pressure" too casually. There are partial pressures of species and total pressure (which is the sum of all partial pressures of all species, regardless of if they're participating in the equilibrium or not).

Partial pressures of reactants and products factor into the equilibrium constant $K_{\mathrm{p}}$. If you increase the partial pressure of a gas that is not participating in the equilibrium, none of the other partial pressures change, so the equilibrium is unaffected, but the total pressure will change. Thus, depending on the circumstances, changing the total pressure may or may not change the position of equilibrium.

The key is you should focus only on the partial pressures of interest. All other pressures are irrelevant, unless they somehow tell you about a change in a partial pressure of interest.