Families follow different rules
Sunrise rule (udaya tithi): the tithi in force at sunrise on the day of the death. Printed panchangs name each day by this tithi, and many families use it.
Time-of-death rule: the tithi in force at the moment of the death. Other families and priests use it. It needs the time.
The two often agree. When they differ, the page shows both and names each rule. Ask your family priest which rule your family keeps.
The Hindu day runs from sunrise to sunrise. A death before sunrise belongs to the day before, so the sunrise rule uses that day’s sunrise.
The yearly day: the tithi of the death comes back once a year, in the same lunar month. The page gives its next two days in the city where you keep the shraddha: the day the tithi is in force during aparahna, the afternoon part of the day used for every shraddha, and the sunrise-rule day when that is another day. The day can differ from city to city, because sunrise and the local time differ.
Which dates it covers
The tool covers deaths from January 1, 2020 to December 31, 2035: the years our calendar tables hold (NASA JPL DE440). For an earlier date, a printed panchang of that year or your family priest can help. Our city month pages start in October 2026, so for an earlier day in any city, such as Sydney, use this tool.
Source
The yearly shraddha on the anniversary of a death: Monier Monier-Williams, Religious Thought and Life in India, Part I (1883), p. 306. The tithi, the paksha and the month come from our calendar engine, with the rule named. archive.org
The yearly day: Dharmasindhu of Kashinatha Upadhyaya (Bombay: Nirnaya Sagar Press, 1888). Its rule for the yearly shraddha of a parent takes the day the tithi is in aparahna, and the earlier day when the two days tie (part 3, pp. 264-266 and 292). The first yearly shraddha goes in an added month when the 13th month is one (p. 266). archive.org
Customs vary. The family priest’s guidance comes first.