Normally people apply these when the Forsythia and Bradford pear are in bloom. This will kill most broad-leaved weeds without killing the zoysia or bermuda. This burns up crabgrass without hurting the zoysia or bermuda. It isn't used on fescue because it burns that too. Nutgrass in the zoysia or bermuda can be a problem.
Image can help to control it, if used according to directions.
This weedkiller kills only grass, and leaves your monkeygrass, ivy, and flowers alone.