That model isn't really suitable for printing in vase mode, so I wouldn't even try it. The author also writes 2 shells, so why not just do that instead?
To really see if vase mode is suitable for a model (other than experience), after slicing in vase mode, you need to inspect the preview in S3D carefully. Even if you have chosen vase mode, it may not be sliced in vase mode. Sometimes it is also necessary to tick the box "Merge all outlines into a single solid model" on the "Advanced" tab to get S3D to really do vase mode. When you do the preview, enable toolhead view and verify that it really is doing vase mode by "playing" the print.