For some reason it saves
That's what is supposed to happen. Magit calls
git commit, which uses the editor specified by
$EDITOR (which Magit arranged to be an
emacsclient instance which connects to the current Emacs instance), the user writes the message and finishes with
C-c C-c. That causes
emacsclient to exit with zero exit status (success) and
git commit then takes the text it finds in
.git/COMMIT_EDITMSG and uses it as the commit message.
every next time when I hit
c in the Magit buffer it opens
.git/COMMIT_EDITMSG instead of commit popup.
That most likely means that you did not finish writing the message by pressing
C-c C-c. Instead you somehow moved away from the buffer. If a commit is in progress, then
c does not show the commit popup. Instead it puts you in the existing buffer so that you can finish writing the message and then press
C-c C-c (or
C-c C-k to abort).