Is the worshiper's action correct in responding to someone who tapped his shoulder, and does his prayer become void if he does that, and what should he have done?

What you did was a correct action, and your prayer is valid, as is the prayer of whoever prayed beside you. It would have been better for him to join you in prayer first, then alert you. What you mentioned, that a worshipper is not allowed to respond to someone who is not praying, is incorrect. Scholars have stated that there is no harm if someone who is not praying corrects a mistake made by someone reciting during prayer. However, it is disliked according to the Shafi'is to pull someone from the row before the puller has entered ihram (definition), lest the one being pulled stands alone behind the row. Rather, one should enter ihram first and then pull. But if this were done, the prayer of none of them would be invalidated.