Before you read the result
What PrivateVPN documents about these signals
The points below are drawn from PrivateVPN's feature page and its help centre. Knowing what each platform is meant to do is what separates an ordinary reading from one worth chasing.
On Linux the kill switch is a firewall you write
PrivateVPN's help centre article for GNU/Linux sets out a manual kill switch, or VPN firewall, built with iptables or with ufw around an OpenVPN connection. It assumes a client file whose remote line uses the server's IP address rather than a hostname, and it notes that iptables rules are wiped on reboot unless you keep them with iptables-persistent or a reboot entry in crontab. If a reading surprises you after a restart, check that the rules are still loaded before anything else.
Those rules cover IPv4 only
Both versions of that Linux guide, the iptables one and the ufw one, are written with IPv4 addresses and commands, and the article does not mention IPv6 at all. On a machine with IPv6 connectivity that leaves IPv6 outside what the rules describe. The IPv6 check on this page is the direct way to see whether your own address is reachable that way while the tunnel is up.
DNS goes through the tunnel
PrivateVPN describes DNS leak protection as ensuring that all DNS requests are routed through the secure VPN connection. Its Linux guide is stricter than many: it declines to allow DNS queries through your default gateway, a shortcut other guides suggest, and leaves that choice to you. A DNS check taken while connected should name a resolver reached through the tunnel, and your ISP's resolver appearing there is the reading to look at twice.
Stealth VPN changes the wrapper, not the result
PrivateVPN describes Stealth VPN as technology designed to make VPN traffic appear like regular internet traffic, for networks that block VPNs. That changes how the connection looks to the network you are on. It does not change what this page reads, which is the address, the resolver and the browser signals your session exposes once the tunnel is up.
Port forwarding opens a door inward
PrivateVPN offers port forwarding for specific services or applications. A forwarded port concerns connections arriving at the VPN address from outside, which none of the checks on this page make. If you enabled it, the address shown here is still the one websites see, and the forwarded port is a separate question for the service you opened it for.