But if there's a fall in aggregate demand at a given price level, there are _fewer_ dollars chasing the same number of goods for a period of time. So if government spending is greater than taxation for that given period, it doesn't necessarily cause inflation.
> the bank exchanges an asset (like a treasury) in exchange for reserves (base money)
The "monetary base" increases because of the way they define the monetary base. In the old days, the money in reserve accounts was convertible into gold, and the money in the Treasury bond accounts wasn't, so they count the money in the reserve accounts as part of the "monetary base" but not the money in the Treasury bond accounts.