Matter over WiFi devices must connect to your WiFi router, that’s the way they send their messages. What they don’t need to connect to is the Internet. (Internet and Wi-Fi are two different things.)
The Matter over Wi-Fi device communicates with your SmartThings/Aeotec hub using the Wi-Fi network in your home. That Wi-Fi network will be managed by your Wi-Fi router.
As far as what the product description at AliExpress should say, you need to understand that AliExpress is just a marketplace for thousands of different individual vendors, most of whom don’t know anything about the technical aspects of what they are selling. (And they often get their goods from returns auctions, or used.) They just copy and paste pictures and descriptions From other places to make their listing based on what they think they have at first glance. So a lot of them get a lot of things wrong.
It’s just too exhausting for me, literally, to go step-by-step through that kind of mosaic.
If you want to ask questions about a matter device, Please find a link to the manufacturer’s official description, either on their site or an authorized reseller.
Or if you want to talk about a specific aliexpress listing, please take it to a different thread than this one. It’s going to be way too specific to fit a FAQ discussion and I won’t be able to help with it anyway. So feel free to start a new thread for that and other people can help you.