I have the same issue too. I use the Netgear Orbi mesh router. I looked into the Netgear community and a lot of ppl are having the same issue too so I suspect is the problem is on the Orbi VPN conf. My VPN conf from Orbi --> Tunnelblick allows me to connect to the printer and print a page, but when I went to ipchicken, my public IP didn't change at all. This is also confirmed by the log in TunnelBlick saying that my IP didnt' change. So I think a lot of users are having issue with the conf file that Netgear Orbi is providing.
I can't read these but please take a look and see if you have any idea why that's the case. INB4: For this set of conf, I have MADE SURE I selected that "all sites traffic and home network traffic" option was selected on my Orbi VPN settings. I also set up the DDNS per instructions found online.
client
dev tap
proto udp
sndbuf 393216
rcvbuf 393216
push "sndbuf 393216"
push "rcvbuf 393216"
remote xxxxxxxxxx.xxxxxxx.xxx 12974
resolv-retry infinite
nobind
persist-key
persist-tun
ca ca.crt
cert client.crt
key client.key
cipher xxx-xxx-xxx
comp-lzo
verb 0
Also, my TunnelBlick log says something like "your DNS is not a known public DNS etc. etc. etc.". But again, I can connect to my printer via my phone tether so the VPN DOES work, it's just the public IP not changing.