I use Shipworks which automatically picks up a CSV based on a timing I choose (every 30min in my case). That's how I get my orders from my sales software (Fishbowl) to my shipping software (Shipworks).
In order to switch to ShippingEasy, I would need a similar feature. The easiest way would be a shared dropbox folder, but I could also set a scheduled task to FTP the CSV.
An auto export for updating locally with tracking numbers would work the same way.