I managed to solve this by using those settings:
(setq magit-diff-auto-show nil) ;; This should be the defult IMHO
(add-hook 'server-switch-hook 'magit-process)
The only problem I got left is that the focus ends in my process buffer and it's not easy (using
other-window) to get back to commit message in the hook, as it's messing with the emacs-client that's being used here.
Still this is good enough for me as now I see the output of pre-commit hook when editing the message.
Following Iqbal's comment I changed my solution to:
(setq magit-diff-auto-show nil)
(add-hook 'git-commit-mode-hook (lambda () (save-selected-window (magit-process))))
which works as a charm!