The documentation above says "Set the SynchronousInputID property of each output to zero".
In the designer the option is: None.
Key thing is you need to:
1) create the script task
2) create the inputs & output
3) set the SynchronousInputID to None on all outputs that you intend to be asynchronous
4) then Edit Script in the properties page.
If you don't follow this precise order, the generated script will be missing the CreateNewOutputRows() method so you will not be able to create your asynchronous output.