You cannot see that very clearly in your Bible, but the phrase "at even" is not ben ha arbayim. It may be translated in your Bible "twilight," but it is not in the Hebrew. It is ba erev. This clearly contradicts the command given in Exodus 12 to kill the lamb at ben ha arbayim.
It is clear that God sent the quail at ba erev. Ba erev is "the going down of the sun." That is exactly what this Jewish Publication Society Bible translation said. It said that this sacrifice He is speaking of in Deuteronomy 16:6 was to be killed at the going down of the sun, at ba erev. The Passover sacrifice was to be killed at ben ha arbayim. Verses 12 and 13 of Exodus 16 show that ben ha arbayim follows bar erev. Because the quail came at ba erev, it took the people a while to catch the quail, to put them to death, and to prepare them to eat. They then had quail after ba erev. Therefore ben ha arbayim comes after ba erev. This is very clear.
Ben ha arbayim does not occur before sunset, nor does it occur at the same time as ba erev. Therefore the sacrifice of the Passover lamb did not take place at ba erev, so whatever sacrifice is being spoken of here is not the Passover lamb sacrifice. Now what sacrifice is He talking about? We shall see. That is three differences already.
Notice the phrase "at the place which the LORD your God shall choose." This clearly contradicts Exodus 12 and Numbers 9 which command a domestically-killed Passover lamb.
Beginning in Exodus 25 we saw all the instructions for the building of the Tabernacle, for the making of the dress of the priests, for all of the furniture, for all of the appurtenances of the Tabernacle, and the consecration of both the priests and the Levites. All of this was given by command in the first month of the second year of the coming out of Egypt. We saw the completion in the story of the Tabernacle, and then the first thing they did was keep a Passover. That is recorded in Numbers 9. There was no change between Exodus 12 and Numbers 9, even though now the Tabernacle existed and the priesthood was installed and consecrated and in its place.
A domestically-killed Passover lamb was still the command after the Temple and the priesthood were in place. This makes it very clear these things that were offered at the Tabernacle, or the Temple, were not the Passover lamb. They were other offerings. That is six differences, with Exodus 12, Numbers 9, Leviticus 23, or Leviticus 33.