Hello,
when I click the "Update cart button" shop does not react, only after I to a page refresh the message "Cart updated" is displayed and the updated cart contents (quantities and prices) are displayed.
The system cache plugin is disabled.
I have Joomla 3.8.8, Eshop Fashion Pro template and Eshop 3.0.3, no other component or module on a local test server, so unfortunately I cannot give you access from outside.
The behaviour is the same on Safari and Firefox.
Sincerely,
Leon