When on the visor window, using the “New Tab > Profile” menu item ignores which terminal profile was selected, and instead always opens a new tab with the default terminal profile.
If you open a new Terminal window with a different profile and drag the tab onto the visor window, opening a new tab with the same settings also ignores the currently-active terminal tab’s profile and again uses the default terminal profile.
I’m guessing this is a consequence of how TotalTerminal forces a specific terminal profile? As I’ve read, it will open with a “Visor” terminal profile if one is defined, otherwise it uses the default profile. It would be fantastic if TotalTerminal could respect the context of these New Tab menu items!
As it stands, if I want to use my “red” terminal profile to remind myself that I’m ssh-ed into a sensitive server, I have to do the whole dance outlined above, where I open a new “red” terminal window and drag the tab onto the visor window. While possible, doing this several times a day gets a bit tiresome! 
Btw, thank you for making TotalTerminal!