I live in Italy - the Quattro Stagioni brand here has been around for more than 30 years, and it is considered the golden standard for in-house canning (other Bormioli glass products are well regarded, too); everyone I know who canned something in his or her life have been using them, and I've never heard of anybody saying anything but great stuff about them. It's rare that I go a whole month without eating something that is coming out of a Quattro Stagioni jar. The one-piece lids are indeed very handy, even if they are a bit pricey (but you probably already noticed that).
All of the Bormioli material (website) and instructions (I'm reading them now from the lid packaging) only mention canning with boiling (pasteurization to be precise), and I've only seen them used that way. This restricts the type of foods you can can (pun not intended) to highly-acidic ones: fruit conserves, tomato sauces, pickled vegetables, etc.
Of course, for maximum hygiene you should follow the instructions to the letter, and use a new cap every time. However, I've seen people successfully re-use caps for canning with less spoil-prone foods (e.g. pickled vegetables), but this is anedoctal and I don't think I can really suggest it.
The lid packaging also report a toll-free number “grandmother Amelia info” (not joking), but unfortunately it's late now as I write; I might call next Monday if I have time.
Happy canning!
No, it isn't safe, water bath canning is only safe for high-acid foods as the acid kills botulism. Low-acid food must be processed at 240F, 116C, and that can only be achieved in a pressure canner.
When you pressure cook the soup it kills the bacteria, however when you then transfer it to the sterilized jars it could be contaminated on the way, and then the water bath won't be hot enough to kill the bacteria.
Best Answer
Since you are asking about canning then what you are describing is not a canning process which will give you a result you can store long term at room temperature. Long-term storage of soup would require pressure canning to raise the internal temperature high enough to kill any foodborne illnesses.
If you plan to freeze the soup then mason jars aren't ideal, they'll work but they are bulky and take up a lot of room. In any case you don't get any real benefit from putting the lid on when hot if you are going to freeze them, you're better off letting it cool so you don't end up overwhelming your freezer's cooling capacity.