Usually, the Add to cart button on Quick View is separate from your themes cart. To integrate with your cart, you need to find the Jquery selector of your cart and paste in Quick View > Settings menu > Custom CSS settings tab > jQuery Selector input field. Then it will be possible to update the shopping cart counter of your theme when customers click on the "Add to cart" button on Quick view popup. 

Step-1: If do you want to update shopping cart count numbers. 

Step-2: Find the Selector of the shopping Cart Count.

Right-click on the shopping cart count numbers and click Inspect

Step-3: Follow the septs according to the below image.

1. Right-click on the highlighted span elements.

2. click on copy menu and copy selector

You've successfully copied the CSS selector.

Step-4: Paste Jquery selector

1. simply go back admin and quick view Settings menu

2. Go to the Custom CSS Tabs settings

3. And paste in Selector of your cart input fields.

4. Save settings and Enjoy!.