Exodus 12:31

And the border of the land of Mizraim extended four hundred pharsee; but the land of Goshen, where Mosheh and the sons of Israel were, was in the midst of the land of Mizraim; and the royal palace of Pharoh was at the entrance of the land of Mizraim. But when he cried to Mosheh and to Aharon in the night of the Pascha, his voice was heard unto the land of Goshen; Pharoh crying with a voice of woe, and saying thus: Arise, Go forth from among my people, both you and the sons of Israel; and go, worship before the Lord, as you have said;

AND HE CALLED FOR MOSES AND AARON BY NIGHT. “This teaches us that Pharaoh went round to the entrances leading into the city, crying out, ‘Where does Moses dwell? Where does Aaron dwell?’” Thus the language of Rashi. Now this happened because Moses and Aaron lodged [close to the vicinity of the palace] that night, [the city of] Egypt, so that Moses’ words would be fulfilled, as he said, And all these thy servants shall come down unto me, and bow down unto me, saying: Get thee out. And when Pharaoh came to them, they sent messengers to the land of Goshen where the children of Israel dwelled, giving them permission to leave, and they all assembled in Rameses. By that time, it was already well into the day. From there they journeyed with a high hand, with Moses at their lead, as it is said, And they journeyed from Rameses in the first month, on the fifteenth day of the first month; on the morrow after the Passover the children of Israel went out with a high hand in the sight of all the Egyptians. The verse stating, The Eternal thy G-d brought thee forth out of Egypt by night [is no contradiction], since from the time Pharaoh gave them permission to go — [which was at night] — they are already deemed as “going forth” from Egypt.
And thus the Rabbis have said in the Sifre:, 128. See above, Note 209, on the word “Sifre.” “Had they not gone forth out of Egypt only at daytime, as it is said, On the morrow after the Passover the children of Israel went out? [How then does Scripture say that we were brought forth out of Egypt by night?] Simply, this teaches us that the redemption [from bondage] took place at night [although the actual exodus took place during the day].” And in the Gemara of Tractate Berachoth we read: “All Rabbis agree that the redemption took place at night, as it is said, The Eternal thy G-d brought thee forth out of Egypt by night, but the actual going forth took place only at daytime, as it is said, On the morrow after the Passover the children of Israel went with a high hand in the sight of all the Egyptians.”
And some scholars say that they went out from [the city of] Egypt at night, and at daytime they went out from the land of Egypt, which is Rameses, for many of them dwelled in the city of Egypt, and they left at night and joined their brothers in Rameses. But this is not correct, since Scripture says, And none of you shall go out of the door of his house until the morning. Thus they were forbidden to go out of their homes at all at night. And similarly the Rabbis have said in the Mechilta: “And he called to Moses, and Aaron by night, and said: Rise up, get you forth. But Moses said to Pharaoh: ‘Thus we have been commanded: And none of you shall go out of the door of his house until the morning. Are we thieves that we should go forth at night? We shall go forth only with a high hand in the sight of all the Egyptians.’”
Now Onkelos explained, was translated by Onkelos thus: “The Eternal thy G-d brought thee forth out of Egypt and did miracles for you at night.” that the miracles which were done for the Israelites on that night make it proper to say that on that night G-d “brought thee forth,” because on account of these miracles, they went forth from Egypt.