I went back and rechecked. If the fan mode is selected, you can only set the fan at one of the three speeds. If you leave it in the fan mode, the dehumidifier will not come on.
Once the fan speed is selected, it will run at that speed in the dehumidifier mode. The fan will keep running, even when the dehumidifier (compressor) shuts down.
The only way to get it to turn off is to use the clock setting, which either selects how long it stands-by before starting , or how long it will run before going back to stand-by. DeLonghi calls it "stand-by," we would call it "off." DeLonghi calls unplugged "off."
I've never turned mine to stand-by, because it will never get my entire house down to 30% humidity (I have it where my air handler returns air to the basement). I live in the greater DC Metro area, where 75% humidity is considered extremely dry.
Apparently the normal mode of operation is fan on unless awaiting a clock start, or encountering a clock shut-down; either condition puts it into the "stand-by" mode.