Yes, they do. You create resources and you delete resources and if you care about cost you creat alarms and tie them to scripts that automatically delete resources.
It’s basic stuff.
Those alarms can take hours to cut in, because AWS does not report costs in real time
Even if you rig up your own spending watchdog which polls the clouds billing APIs, you're still at the mercy of however long it takes for the cloud to reconcile your spending, which often takes hours or even days.