... When Julius Caesar established his calendar in 45 BC he set March 25 as the spring equinox. Since a Julian year (365.25 days) is slightly longer than an actual year the calendar drifted with respect to the equinox, such that the equinox was occurring on about 21 March in AD 300 and by AD 1500 it had reached 11 March. This drift induced Pope Gregory XIII to create a modern Gregorian calendar. The Pope wanted to restore the edicts concerning the date of Easter of the Council of Nicaea of AD 325. (Incidentally, the date of Easter itself is fixed by an approximation of lunar cycles used in the Hebraic calendar, but according to the historian Bede the English name 'Easter' comes from a pagan celebration by the Germanic tribes of the vernal - spring - equinox.)

So the shift in the date of the equinox that occurred between the 4th and the 16th centuries was annulled with the Gregorian calendar, but nothing was done for the first four centuries of the Julian calendar. The days of 29 February of the years AD 100, AD 200, AD 300, and the day created by the irregular application of leap years between the assassination of Caesar and the decree of Augustus re-arranging the calendar in AD 8, remained in effect. This moved the equinox four days earlier than in Caesar's time ...

"Gregory dropped 10 days to bring the calendar back into synchronisation with the seasons. Accordingly, when the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of ten days. The Julian calendar day Thursday, 4 October 1582 was followed by the first day of the Gregorian calendar, Friday, 15 October 1582 (the cycle of weekdays was not affected)." (Wikipedia)

However, the Gregorian calendar was not accepted at once everywhere:

"The reform was adopted initially by the Catholic countries of Europe. Protestants and Eastern Orthodox countries continued to use the traditional Julian calendar and adopted the Gregorian reform after a time, for the sake of convenience in international trade. The last European country to adopt the reform was Greece, as late as 1923 ... Britain and the British Empire (including the eastern part of what is now the United States) adopted the Gregorian calendar in 1752, by which time it was necessary to correct by 11 days. Wednesday, 2 September 1752, was followed by Thursday, 14 September 1752. Claims that rioters demanded 'Give us our eleven days' grew out of a misinterpretation of a painting by William Hogarth." (Wikipedia)

But we can assume it was the Gregorian (and not the Julian) calender which was brought to Easter Island when the missionaries arrived.

Still, there could have been a knowledge on the island of how the Julian year continued to be used in astronomy:

"In astronomy, a Julian year ... is a unit of measurement of time defined as exactly 365.25 days of 86,400 SI seconds each. The Julian year is the average length of the year in the Julian calendar used in Western societies in previous centuries, and for which the unit is named. Nevertheless, because an astronomical Julian year measures duration rather than designating a date, this Julian year does not correspond to years in the Julian calendar or any other calendar. Nor does it correspond to the many other ways of defining a year ...

Before 1984, both the Julian year and the mean tropical year were used by astronomers. In 1898, Simon Newcomb used both in his Tables of the Sun in the form of the Julian century (36,525 days) and the 'solar century' (36,524.22 days), a rounded form of 100 mean tropical years of 365.24219879 days each according to Newcomb.

However, the mean tropical year is not suitable as a unit of measurement because it varies from year to year ... In contrast, the Julian year is defined in terms of SI units so is as accurate as those units and is constant. It approximates both the sidereal year and the tropical year to about ±0.008 days. The Julian year is the basis of the definition of the light-year as a unit of measurement of distance ...

The Julian year, being a uniform measure of duration, should not be confused with the variable length historical years in the Julian calendar. An astronomical Julian year is never individually numbered. Astronomers follow the same calendar conventions that are accepted in the world community: They use the Gregorian calendar for events since its introduction on October 15, 1582 (or later, depending on country), and the Julian calendar for events before that date ..." (Wikipedia)

By the way, when I fetched right ascension data for stars from Wikipedia they were defined by the positions in the year 2000, or properly speaking in the epoch J2000.0:

"In astronomy, an epoch specifies a precise moment in time. The positions of celestial objects and events, as measured from earth, change over time, so when measuring or predicting celestial positions, the epoch to which they pertain must be specified. A new standard epoch is chosen about every 50 years.

The standard epoch in use today is Julian epoch J2000.0. It is exactly 12:00 TT (close to but not exactly Greenwich mean noon) on January 1, 2000 in the Gregorian (not Julian) calendar. Julian within its name indicates that other Julian epochs can be a number of Julian years of 365.25 days each before or after J2000.0. For example, the future epoch J2100.0 will be exactly 36,525 days (one Julian century) from J2000.0 on January 1, 2100 (the dates will still agree because the Gregorian century 2000–2100 will have the same number of days as a Julian century).

Because Julian years are not exactly the same length as years on the Gregorian calendar, astronomical epochs will diverge noticeably from the Gregorian calendar in a few hundred years. For example, in the next 1000 years, seven days will be dropped from the Gregorian calendar but not from 1000 Julian years, so J3000 will be January 8, 3000 12:00 TT." (Wikipedia)