What is a tithi birthday?
Traditionally a birthday is kept on the tithi (lunar day) of birth in the same lunar month. Because the lunar year is shorter than the solar year, that day moves on the civil calendar every year.
Shraddha is offered on the tithi of the ancestor's passing, at aparahna (afternoon), every year, and again in Pitru Paksha on the same tithi of the dark fortnight of Bhadrapada.