As a result, the two of us who started off being very poor in programming wound up writing and designing the main structure of a website called “team work”. I continued to be in charge of technology when it came to the stage of APP exploration.
I mean when the main part of the website has been completed, we started to design APP. Usually "when it come to.." is followed by a specific event, not by a word related with time. So I am not sure at all whether it is natural to say "when it comes to the stage of..."