Some sites say that I'm in a different place than the one selected on the VPN
We're aware of this problem. This is caused by how Google assign country to particular IP. If you'll be routed to VPN server used mostly e.g. by Ukrainian people and Google classified such IP as Ukraine then you'll be hit by this issue where google.com is redirected to google.com.ua.
Replace Google by any site. Basically the site is guessing your location wrongly.