To understand how the receipt of new reserves influences a bank's behavior, the place to start is to ask whether the bank is willing to hold the reserves overnight. Prior to 2008, a bank could earn no interest on reserves, and could get some extra revenue by investing any excess reserves, for example, by lending the reserves overnight to another bank on the federal funds market. In that system, most banks would be actively monitoring reserve inflows and outflows in order to maximize profits. The overall level of excess reserves at the end of each day was pretty small (a tiny sliver in the above diagram), since nobody wanted to be stuck with idle reserves at the end of the day. When the Fed created new reserves in that system, the result was a series of new interbank transactions that eventually ended in the reserves being withdrawn as currency.
All that changed dramatically in the fall of 2008, because (1) the Fed started paying interest on excess reserves, and (2) banks earned practically no interest on safe overnight loans. In the current system, new reserves that the Fed creates just sit there on banks' accounts with the Fed. None of these banks have the slightest desire to make cash withdrawals from these accounts, and the Fed has no intention whatever of trying to print the dollar bills associated with these huge balances in deposits with the Fed.