I checked out the site and I don't think it's authoritative.
 
Firstfruits is calculated from the new moon after the vernal equinox.  Neither of those points depends on the Gregorian calendar.  As I understand it, the numbering of the days shifted by ten with the calendar correction in 1752, but the sequence of the days was unaffected.  In other words, Wednesday September 2nd was followed by THURSDAY, September 14th.  They didn't count forward twelve days and designate September 14th as a Monday.  This preserves the order of the days from antiquity.
 
This means the order of the days in Biblical times has stayed the same.  And this means the calculation of Pentecost was unaffected by the calendar change.  Pentecost was and remains the day after the seventh sabbath following the weekly sabbath after Unleavened Bread.  And since this year is a "year of perfect order" we see Nisan 10 on the first day of the week, Passover on the 14th, Unleavened Bread on the 15th, a weekly sabbath on the 16th, and Firstfruits on the 17th.
 
Fifty days after the weekly sabbath brings us to Sunday, May 31st.
 
The question of the correct date for Shavuot/Pentecost arises from a dispute between the Pharisees and the Sadducees regarding which sabbath is in view from which the 50 days are calculated, since Passover week has two sabbaths:  Unleavened Bread being the "high" sabbath and the day after that being the weekly sabbath.  The Sadducees got this one right, it appears.  But even if not, it moves Pentecost only one day.
 
We'll know the answer to that in less than 40 hours.
 
Very best,
 
Steve