Your character does not have to provide activity for first month of the activity period (July, in this case), since they were accepted into the game during that month. The character will have to provide activity for the month after, though. So, 15 comments over three threads maximum, or 20 comments over four threads maximum for the month of August will be needed for your character when the Activity Check happens. Comments from July will not be accepted in place of August activity.

Sorry about the confusion, and I hope this helps clear things up!