Checkout address fields not update correctly

Hello, I have installed your plugin on smartprotection.ro and seems to work fine. The only problem I have meet until now is the update of billing info city fields.
On my /checkout page the fields are working fine and the city’s are loaded well after the country and state/region have been selected.
On the the plugin cart window the city is not preloaded. I select country and state and after that I don’t have city’s charged on the lists based of state selected above. I was purge all cache but still the same.
You know if your plugin use other form of billing/shipping address fields then the woocommerce standard one?
Can you help me to check this problem?
Thanks.