Syncio does not push payments or sync shipping settings between stores so the actual shipping cost charged to customers is set in the destination store's Shopify settings and charged only in this store.

When using the Orders add on why is there an "add shipping cost" field when i push orders?

This is meant for record-keeping purposes so that the sale total includes shipping cost if needed. The app pushes the accurate shipping amount via the settings during the order push (or, if automated, in the settings).