Just to reinforce it - you want to be continuosly purging the cup with argon, not just filling it once and thats it.
Yes.
You should also take some steel wool roll it into a small ball and tape it to the end of your purge hose. This will diffuse the Argon as it comes out of the hose. If you don't the Argon will flow straight out of the hose and create turbulence inside the purge box, can, or whatever you use.
Since you will be removing a small volume of Oxygen, the purge gas only needs to be set at 10 to 20 on the flow meter.
You will also want to stick some steel wool in the end of the fitting you are welding in. That will allow the Argon to vent out yet still maintain shielding of the weld.
Wait for a few minutes too, once you start the flow of back gas. Give the Argon time to push out the Oxygen. The longer the better.
Make sure you tape(masking tape works very well) to seal the cup and where the hose enters the cup very well. Don't leave any cracks for the Argon to seep out, or create a vacuum sucking in more Oxygen.
If you have any other questions feel free to ask, I've welding for 23 years.
I've done xray quality welding in chemical plants on all types of metals especially stainless for close to 15. I also weld for some of the local breweries.