The water should not continue flowing after the container is full. the auto shutoff should take care of that part. If it is not it is either defective or you have it plumbed wrong.
Three quarters of the way down the link, is a schematic (simple) that might help you. I do not have this brand of ro, just use it as a helper.
http://www.watergeneral.com/support/pdf/RO585.pdf
Take the 5th stage as if it was the DI then into the 45 gal drum
Delete the storage tank they have, unless you have one and attach it to the icemaker/drinking faucet
And I agree, if you are using this unit for drinking, tee off the drinking water before the DI