You should be able to add `cider--debug-mode` to the `evil-insert-state-modes` list so that you automatically enter insert state when the debugger is triggered.  I tried the following but it doesn't work.

    (add-to-list 'evil-insert-state-modes 'cider--debug-mode)

I haven't dug into why this isn't working, but for the time being I'm using the `cider--debug-mode-hook` which is called whenever you enter or leave the mode.

    (defun my-turn-on-insert-state ()
      (if cider--debug-mode    ;; Checks if you're entering the debugger   
          (evil-insert-state)  ;; If so, turn on evil-insert-state
        (evil-normal-state)))  ;; Otherwise, turn on normal-state


    (add-hook 'cider--debug-mode-hook 'my-turn-on-insert-state)


This assumes you want to be in normal-state whenever you exit the debugger.