Numbers 33:3’s summary of the Exodus event varies with the account in Exodus 12 on two points.
First, within the Priestly tradition itself there seems to have been a discrepancy on the date assigned to the actual Exodus. Was it the 14th, that is Passover, or the 15th, that is the following day? Indeed this discrepancy may have actually been more of a discrepancy on calculating when day begins.
So while Numbers 33:3 makes it pretty clear that the Israelites left Egypt on the morrow of Passover, on the 15th that is, Exodus 12:14-19 make it just as clear that it was “this day” (Ex 12:14, 12:17), that is the 14th of the month, Passover. This discrepancy is even transferred to the parallel discrepancy concerning the Festival of Unleavened Bread: does it commence on the 14th or the 15th?—treated already in contradictions #113 & #194-197.
Second, while Numbers 33:3 claims that the Israelites left Egypt on the day after the Passover and in full view of the Egyptians (“before the eyes of all Egypt”), the traditions preserved in Exodus 12 recount how the Israelites left during the night, in haste and practically in stealth.
On a rhetorical level the claim made in Numbers 33:3 amounts to hyperbole. But it also serves a theological purpose: now all of Egypt knows who Yahweh is! Remember that theologically speaking the central issue of the Plague narrative, especially in the hands of the Elohist, was “who is Yahweh?” (Ex 5:2). Of course Pharaoh’s seemingly innocuous question gets a response from Yahweh: “And Egypt will know that I am Yahweh when I reach out my hand against Egypt” (Ex 7:5, etc.). And indeed by the end of the 10 plagues, the Pharaoh and all of Egypt know who Yahweh is—the theological purpose and message of this story!