I have never figured out how to get a string to wrap the tuning pin only a small number of times. In this photo, the C string is original to the instrument. The D string I just put on wrapped the pin 5 times before it started coming up to pitch. How do I get just 3 wraps for the new string?
If this is a nylon string, it will continue to stretch out for some time. The more you tune it, the sooner it will finish stretching and hold pitch. You can unwind it, pull it taut through the hole, and wind it up again. You may need to do it more than once over several days.
Then cut off the excess. There is no rule on how many turns can be on the tuning pin as long as you don’t let them push up against the neck. Always avoid having the string wound up against the neck because it will act as a force pulling the tuning pin tighter into the neck, which can cause trouble in the future.