when I insert a LaTeX environment with the cdlatex keybinding C-{, the environment is not properly indented as the rest of the text and the TAB key is bound to the cdlatex functions. Is there a way to get it properly aligned directly, without having to select the region and press TAB?

I would like to achieve a real indentation and not a virtual one as provided by org-indent-mode. Therefore org-indent-mode is nil and org-adapt-indent is t (as per the default config).