The package has code like this:
(defvar tablist-mode-map
(let ((kmap (copy-keymap tablist-minor-mode-map)))
(set-keymap-parent kmap tabulated-list-mode-map)
As far as I understand, this means that if the user adds his bindings to tablist-minor-mode-map, they won't be added to tablist-mode-map. If you consider that a problem, you could rewrite your code that way (untested):
(defvar tablist-mode-map
(let ((kmap (make-sparse-keymap)))
(set-keymap-parent kmap (make-composed-keymap tablist-minor-mode-map tabulated-list-mode-map))
I'm not an expert so please double-check :-).