Those containers will work, and are probably appropriate if you are going to try and ferment in the same container you no-chill in. You would need the headspace.
I don't use that type of container and its not my opinion that they are the best type of container. I use this type of HDPE jerry can (willow brand, Kmart)
and a lot of people use a more square rather than narrow version that looks like this
Both these containers allow you to squeeze out excess air and limit the chance of oxidation of the hot wort. Not really an issue if you are going to ferment the next day I guess - But I would prefer to have teh air squeezed out if I was going to be storing the cube unfermented for any period of time. I often leave mine for weeks or months before I ferment them and so I want the air out.
You do it like this (roughly) and that would be harder to manage with a round NC container, especially one with significant headspace.
Mine are 20L nominal capacity (actually hold about 24L) and are perfect for filling a corny keg or a little more.
I also wouldn't bother with putting them in the fridge - its only going to work the hell out of your fridge and it still wont chill them fast enough to get any "rapid chill" benefits .. so why waste the power? I just leave them to chill down at ambient. It'll be cool enough to pitch inside 24hrs - gives you time to grow a starter.
Like I said, there are different ways to manage this - the guy in the link you posted is doing perfectly well, so who am I to say he's wrong. I don't do it like that for a number of reasons that I have detailed.
Oh - and I filled my cubes up with very hot water and allowed them to cool down - several times before I put wort in them. I kept doing it till I couldn't taste the difference between water boiled and cooled in the cube, and water boiled and cooled in a glass beaker (blind triangle tasting) that way I was sure there weren't going to be any plastic flavours transferred to my beer. Other people have not bothered doing this and have had no problems - but I like to be careful.
Thirsty