I mentioned on the feedback/suggestions thread (in the original post) that the intention is that the Pet Event notification only appears once you have completed a battle or opened the game to the World Map in case you were wondering 
Originally this design choice was made because we wanted to make the notifications to not be obtrusive (i.e. appearing during a battle…). However, if the above is not true, have you left Gems open, but minimised, or have you completely launched the game but been unable to jump in?