That's not full truth. In the last 20 yeas central banks do their big and sudden moves using "Open Market Operations". They buy or sell money like assets in market and effectively increase or limit the quantity of money.
Basically, the central bank sets an interest rate target and then performs open market operations until the interest rate matches the target.
That obviously affects the quantity, but the point is that the target is the interest rate. The quantity just ends up being whatever happens to be necessary to hit the interest rate.
When you reduce the volume of assets available, or the price renting the asset, you increase it's value. In this case the asset is money.
Market interest rate is a signal how effective the action is long before inflation statistics is available.