Can Allah expose in this worldly life a person who disobeys Him secretly, such as someone who masturbates or commits any other sin in private, and how would this exposure be if it were to happen?

Allah Almighty is Hayy (Shy) and Sittir (Concealer of faults), He loves shyness and concealment. This is indicated by the Hadith: "Indeed, Allah, the Most High, is Hayy (Shy) and Sittir (Concealer of faults), He loves shyness and concealment." Allah may conceal the faults of His believing servant who commits a sin, both in this world and the Hereafter. Allah may also remove His concealment from some people, either as a hastened punishment, a warning, or a lesson. There is a disagreement among scholars whether Allah exposes the disobedient person from the first instance or after repeated transgressions.