The import is not a syncing service. It allows you to take the listings you currently have on one website and clone them in Nembol so that you can share them on many more.
You can then create all your new listings in Nembol and publish them on all channels at once. Nembol receives sale notifications from most channels, however due to some channels' API restrictions, this is not always the case. When you make a sale on Etsy or in store, for instance, quickly delist the product from all selling channels with a single action using the Nembol's Delist button.