One of the issues that has been addressed regarding this Rashi is that it seems contradictory to another Rashi. When commenting on the events of Krias Yam Suf, Rashi mentions that it happened on the seventh day of the Exodus. Rashi even states that this is the basis for the custom to read the Torah portion of Krias Yam Suf on the seventh day of Pesach. (Rashi Shemos 14:5)
I would like to offer two suggestions that our founded on how to calculate when one's day begins. The first answer is suggested by Rabbeinu Bachye. He maintains that even though Jewish law usually recognizes night as preceding day, when it comes to sacrificial offerings the day comes first (regarding sacrifices, the portion placed on the Mizbeach is able to be burnt the night following the day in which the blood was sprinkled).
Our Exodus began on the 14 of Nisan when the Korbon Pesach, a sacrificial offering, was brought in the early afternoon. Thus, the morning of what we would refer to as the seventh day of Pesach is actually the eighth day from the Exodus if one is utilizing the sacrificial offering system. In this regard both the Rashi that maintained that it was day seven and the one that states that it was day eight are correct, they are just describing the event based on separate systems. (Rabbeinu Bachye Bamidbar 15:41)
Seeming to support this assumption is the fact that the Rashi that maintained that it was day eight focused on the time when Klal Yisrael sang and not when the Egyptians perished in the sea. They perished just before morning, (Shemos 14:27) but we did not sing until after daybreak. (Rashi Shemos 14:5) Unfortunately, Rabbeinu Bachye leaves hidden the reason why Tzitzis reflect the sacrificial offering system and the Torah portion read on Pesach reflects the regular system.
Before presenting another approach I would like to say, as an aside, that it is pretty fascinating that the evening during which the sea split had a very rare occurrence happen in the sky. That night the moon partially blocked Mars making it appear as if the two were touching (I know that I posted a similar thing with Saturn regarding the first Tisha B'Av earlier this week, but these events truly are rare which makes it even more fantastic that they seem to happen on these monumental dates in Jewish history). Astrologically, this event portends malevolent tidings. (Ibn Ezra Reishis Chachma 7) Interestingly, it occurred in the constellation Aquarius which is considered the be the mazal of Klal Yisrael. (Ibn Ezra Shemos 31:18) Aquarius, depicted as a man pouring a bucket of water, would have been seen as being afflicted by this sign. It seems interesting that Hashem bestowed His mercy that evening and saved this young nation. Just as he split the water of the Yam Suf, he "split open" the evil tidings found in the constellation of water that symbolized this nation and protected them miraculously. In fact, quite unbelievably, Rabbeinu Bachye mentions that the Jewish nation should have perished at the Yam Suf because the Egyptians had tapped into the inlfuence of Mars which is associated with death. It was only because of God's tremendous mercy that he saved us. (Rabbeinu Bachye Shemos 14:25)

I am certainly not qualified to argue with Rabbeinu Bachye, but I would like to suggest an alternate way one could have read Rashi based on the Meiri. The Meiri states that their are four accepted ways that civilizations have decided to begin their days. One is the Jewish way and that is the start from evening. A second way is to start from daybreak. Another is to start at midnight (like is the practice here in the U.S.) and the last way is to start from midday when the sun is at its peak. This last way, says the Meiri, is based on deep astrological meaning and this is how the ancient Egyptians began their day. (Meiri Pesachim 5a)
Rashi mentions that Paroh sent a messenger with us when we left Egypt to make sure that we would return after three days. When we did not, Paroh came out with his armies and advanced towards our camp on days five and six. The night of the seventh day of our Exodus his battalions were drowned in the sea. (Rashi Shemos 14:5) In fact, this is the same Rashi that mentions the reason for reading this portion on the seventh of Pesach.
The Sifri mentions that we left Egypt at midday. (Sifri Devarim 337) Rashi quotes from this Sifri elsewhere implying that he is of the same opinion. (See Rashi Bereishis 7:13) If Rashi agreed with the Meiri then Paroh sent his messenger with us right at the "beginning" of the first day which coincides with 15 Nisan in the Jewish calendar at midday (this is the day after the Korbon Pesach and the first day of our holiday of Pesach). That means that seven Egyptian days after would have the Egyptian destruction occurring on the night of the eighth day of the Jewish count. Since we do not follow the Egyptian calendar we commemorate this event with the seventh day based on our count and we read the Torah portion of this event on the seventh of Pesach. The Rashi at the end of our Parsha, though, would also be accurate. The Egyptians perished on what we would call the eighth day, but the seventh Egyptian day from our Exodus.