Jenkins behind nginx reverse proxy doesn't redirect in all situations
After a fair amount of reading around the following helped my situation.
proxy_set_header X-Forwarded-Host $http_host;
This maintained the port number and functionality seemed to be as expected with Jenkins.
Regarding the reverse proxy is broken, I inspected via curl the administration task. This failed and was giving me the error and redirected me here: https://curl.haxx.se/docs/sslcerts.html. Even though all browsers show the secure icon and show no problems.