My husband had been baptized at 13 (ish). He said he thought he got baptized because he knew his mom wanted him too. I am sure he knew some of what was right and wrong, but was not was not privy to a lot of Bible teaching. (He was later baptized from the heart after we were married). Do you think he was a Christian before he was baptized (for lack of a better word) the second time?
Your question is one that I can't personally answer because I can't look into a person's heart. I can only go on what I am told. But the real question is: does it matter as far as his condition of salvation today?
For a person to be saved, God requires that they have faith -- a faith that is based on what God has taught (Romans 10:17). No one knows everything when the chose to become a child of God, even after a lifetime of learning there remains much that still could be learned. However, there are certain ideas that critical: a belief in the existence of God, a belief that God can save (Hebrews 11:6), a belief that Jesus is the Son of God, a belief that Jesus died for our sins, and a belief that Jesus was resurrected and is now alive in heaven ruling over his kingdom are just a few examples.
To be saved, a person needs to know he needs rescuing. That means he needs to understand something about sin and that he is guilty of sin. After all, if you don't think you have sinned, then why would you seek to be saved from your sins? The knowledge must be of the kind that a person doesn't want to stay in sin, but is eager to leave sin behind. This is repentance (II Corinthians 7:9-11).
Paul also says that confession is needed (Romans 10:8-10). Confession means a willingness to stand up for what you believe. To claim belief but to not stand up for it isn't true belief (Matthew 10:32-33).
Baptism is then the opportunity to enter into a covenant with God (Colossians 2:11-13). At that point a person becomes a child of God (Galatians 3:26-27). And God gives him forgiveness of his past sins (Acts 22:16; Romans 6:3-7).
Without faith, repentance, and confession baptism becomes a meaningless dunking in water.
It is difficult with a young person to tell if they truly are converted to Christ when they ask to be baptized. I usually ask them several questions to see if they have some understanding. If they don't, I suggest they wait until they can answer those questions. But if they are determined, I can't justly stand in their way.
At times people come to me to say that they aren't certain that a baptism they did as a young person was legitimate. Again, I will ask them a number of questions to see if they understood what they were doing. It is hard to answer because the intervening years color the responses. However, when we are done I ask if there is any doubt. If there is, I will suggest they get baptized again. At worse, they get wet again for no particular purpose in God's sight. At best, they correct a mistake from their past and can walk forward now with confidence.
As I said, does it matter? Which ever way, saved at 13 or saved as an adult, the point is that now, this day, he is saved. And that is all that matters.