I don't want to add to your worries Masha (although I fear I'm going to!) but after checking out your link, this looks very similar to a plaggy greenhouse I was gifted last May.
The frame looked a bit flimsy to me, so I sank metal poles to a depth of about 3 feet, and lashed the corner poles to these.
The first good blow saw the whole thing do a Mary Poppins across two rows of gardens, reducing it to a pile of junk. All the ties and eyes ripped right out of the cover at the same time.
All may not be lost, however. What I would suggest is to make a frame out of scaffolding boards, the same size as the base. Fasten this down to well knocked-in posts or scaffold poles, and then use battens to affix the bottom edge of the cover to the inside of the frame. This way the wind can't get under it (the sides are too short to bury in typical polytunnel fashion).
It might sound like a bit of a palaver, but it's infinitely preferable to losing the whole thing in a stiff breeze.