Lowering consumption, and increasing savings can increase net exports. Since savings increase relative to consumption, there is more money to lend out to the world (in an open economy), and less investment domestically. The decrease in demand for your currency due to the reduction in investment and rise in savings can lead to a reduction in the real exchange rate for your currency relative to other currencies. NX (net exports) = S - I (Savings - Investment). S = Y-C-G (income - consumption - government spending). As you can see, the level of consumption directly impacts savings. A decrease in consumption increases savings, which in turn decreases the real exchange rate for your currency, which can make imports more expensive, creating nominal price inflation.
Another determinant of inflation however is also the money supply, and this is the biggest factor. The central bank in your country has the largest impact on money supply. This is because Y (output) is fixed based on the factors of production. % change in M (money supply) + % change in V (velocity of money) = % change in P (price level) + % change in Y (output). That is (% change M + % change V = % change P + % change Y). As you can see, the price level directly has to increase proportionately to the change in the money supply that the central bank can manipulate. So even if consumption decreases, nominal inflation rates will rise if the central bank is expanding the money supply. That is how it’s possible to see a decrease in consumption, and still potentially see inflation.