And for those wondering, the answer is YES, the Memorial that Jehovah's Witnesses observe is technically on the wrong day, but it isn't totally their fault.
Jehovah's Witnesses did not originate the "annual" practice of observing communion/eucharist on Nisan 14. The idea is partially based on Quartodecimanism, a practice of the early Jewish Christians who observed the Mosaic Law since it was part of their culture and around Easter they celebrated Passover with all the rituals beginning on Nisan 14. They would follow through the rest of the days with the Feast of Unleavened Bread, etc, and of course begin with a seder.
Since the Jewish Christians observed Passover once a year, some Gentile Christians argued that the Church at large should observe the Eucharist/Holy Communion only once a year on the same date. But this was eventually argued against as Gentiles were not required to follow the law (and Passover is not Holy Communion and not a ritual for Gentiles).
Some Adventists, from whom the Bible Students sprang, experimented with returning to observing the Eucharist in a "purer" form, but chose to have it quarterly instead on annually. Jehovah's Witnesses, however, as they pulled away from the Adventists, decided it should be observed annually.
But why did they choose Nisan 14 and not 15 since the Jews observe Passover on the 15th?
It's not entirely clear, but as long as you remember this text, we can straighten things out for everyone (I will use the NWT this time):
In the first month, on the 14th day of the month, at twilight is the Passover to Jehovah. On the 15th day of this month is the Festival of Unleavened Bread to Jehovah.--Leviticus 23:5, 6.
So as long as you remember that the "Festival of Unleavend Bread" is on the 15th, then everything is going to be fine.* Let's begin...
On the first day of the Unleavened Bread, [Nisan 15] the disciples came to Jesus, saying: “Where do you want us to prepare for you to eat the Passover?”...When evening came, he was reclining at the table with the 12 disciples.--Matthew 26:17-20, NWT.
Now on the first day of the Unleavened Bread, [Nisan 15] when they customarily offered up the Passover sacrifice, [Nisan 14] his disciples said to him: “Where do you want us to go and prepare for you to eat the Passover?”...After evening had fallen, [Nisan 15] he came with the Twelve.--Mark 14:12, 17, NWT.
The day of the Unleavened Bread [Nisan 15] now arrived, on which the Passover sacrifice must be offered [Nisan 14]; so Jesus sent Peter and John, saying: “Go and get the Passover ready for us to eat.”--Luke 22:7-8, NWT.
Now most people who are not Jewish often never notice these differences. They might read past this thinking they are talking about one in the same thing. But the sacrifice of the lamb would take place one day and then everything would close down on the next because it was a Sabbath.
“‘On the 15th day of this month is the Festival of Unleavened Bread to Jehovah. Seven days you should eat unleavened bread. On the first day, you will observe a holy convention. You should not do any hard work. But you are to present an offering made by fire to Jehovah for seven days. There will be a holy convention on the seventh day. You should not do any hard work.’”--Leviticus 23:6-8, NWT
People had to have all the lambs slaughtered on Nisan 14 and prepared because by the time one sat down to eat the Passover Seder, it was Nisan 15, and a Sabbath. No work could be done. You had better have your lamps lit and fires going because you could not light new ones until the next evening. You had to have enough food to last you until the next day too, because you could not prepare new food. That was work, and you could not work on the Sabbath. Nor care for a dead body or bury it.
Thus the "Festival of Unleavened Bread" is when you eat the Seder, the event that occurs on Nisan 15. On the afternoon before then, on Nisan 14, as Josephus reported in War of the Jews, lambs were prepared by the thousands for the Passover meal that would begin that night, which was...Nisan 15.
With the Temple gone and after the Diaspora, the Seder plate now carries merely a shank bone in remembrance of those days (and perhaps to mourn the fact that it is gone). There is no more lamb cooked for Passover meals (soup, chicken and sometimes brisket has come to replace it).
Nisan 14 is still important. On that day Jewish houses are cleared of all last remnants of Chametz or leaven, the last preparation in making a house "kosher for Passover."
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*--I already discussed above that for the sake of catechesis, in the gospel of John, the author takes up the theme "the Lamb of God," and for the this reason, unlike in the Synoptic Gospels, the date for Jesus sacrifice is moved to Nisan 14, the same day that the lambs are slaughtered. This is why I am only concentrating on Matthew, Mark, and Luke, for these gospels state that Jesus died on the night of the Passover Seder meal, Nisan 15.
