Structural shocks that affect the economy will always affect both inflation and output. Your interpretation relies on an intuition where you exogenously vary GDP, keeping everything constant. But this does not happen as inflation will move and this equilibrium behavior will take the Taylor rule into account. Take a positive TFP shock. It will increase output and decrease inflation. Depending on the strength of the responses and the respective weights in the Taylor rule, the nominal interest rate might decrease and thus negatively comove with output.
This is also the reason why, after a positive monetary policy shock, it can happen that the nominal interest rate decreases.