Does the app automatically detect new orders for its basis of recommendation?

I just received a new batch of orders today and I am wondering if the app would process them right away so that it can use them as a basis for upselling items?

The answer actually depends on you. You can set the app to automatically process new orders or you can do it manually at any time convenient to you. All you need to do is enable or disable this feature within the app anytime and make sure to save the settings afterwards.

Check out How to automatically process orders for product recommendations for detailed instructions.