When there is a cash payout scheme, the disposable income increases, so the consumption expenditure increases, and thus the aggregate demand increases. The price level and the output level will increase in the short run. (Note that it counts the consumption expenditure, but not government expenditure)
The inflationary gap will result in an upward pressure on the input prices. In the long run, wages will adjust upward and the SRAS will decrease. The price level will increase and the output will restore to its original level.