The pain or sensation that you feel when you are digging your finger into the bellybutton is caused by the wind in your intestine which travels into your lower abdomen. Your butt and testicles are tuned to feel sensations in that area very strongly in order to maximise their functions, i.e., defecating and sexual arousal.
You sure that's your finger?
You sure that's your belly button?
You sure that's your belly button?
When you did your finger nail in you can almost touch you umbilichs and I have an outie I love it and play with it all the time.