I know that verse well, it is not only sexual desire that will stimulate masturbation. Lots of girls and woman maturbates and women are not stimulated so much by the visual. It is natural desire that comes from within. The sexual desire that God created us with is one of the strongest on earth. Song of Solomon 8:6 "6 Set me as a seal upon thine heart, as a seal upon thine arm: for love is strong as death; jealousy is cruel as the grave: the coals thereof are coals of fire, which hath a most vehement flame.
7 Many waters cannot quench love, neither can the floods drown it: if a man would give all the substance of his house for love, it would utterly be condemned."KjV

Masturbation starts usually as soon as the sexual awakening takes place, in the early teens. The problem is not masturbation but that the world corrupted God's ways. In the Bible people got married as soon as the sexual awakening started.

Question: "How old was Mary when Jesus was born?"

Answer: While the Bible does not specifically state how old Mary was when Jesus was born, most Christian historians speculate that she was around 15—16 years of age at the time of Jesus’ birth. According to Jewish customs at the time, a young woman might become betrothed to a young man as early as 12 years of age, though the consummation of their marriage through ceremony and physical intimacy would not happen until they were legally married, many months or even years later.
https://www.gotquestions.org/how-old-was-Mary.html

So that was God's way, but then the world comes and say no you have to go to school before you can get married, then it was high school, then is was, you must study even further, go to university. Then materialism take over even more and now you must have a car, a house etc etc. and society is going from bad to worse. Now we sit with this problem to stay celibate for years and years after the sexual awakening and most people don't know what to do with this strong sexual desire that God created them with. I believe that masturbation in moderation, not an addiction to it, is a natural way to help young people to stay away from immorality before marriage. If you do not masturbate it even occurs in your sleep to give you release. My remedy for masturbation is, as soon as you met a person you love, get married. I think parents should encourage that even if the person is still studying.
1 Corinthians 7: 9 "But if they cannot contain, let them marry: for it is better to marry than to burn."
I got married at the age of 18 just after finishing my high school. My brother married at 20 because as a devoted Christian he told my parents that he got the wife that God chose for him and that he will not sin in having sexual relations with her, he will marry and finish his studies at the university and he did just that.