After upgrading to 6.2.X, I had a very similar issue. The API returned http instead of https:, but mine was at login. I finally came up with a solution. I am on NGinx, but I would assume that Apache has a similar setting somewhere.
The fix involves changing the NGinx config file for the site. Replacing
proxy_set_header Host $host; with proxy_set_header Host $host:$server_port; did the trick.
More details on the problem can be found here.
Since upgrade, WebUI redirects with NGinx on alternate listen port [Possible Bug] [Work-Around].