The interpretation is based on two strong pieces of evidence:

1. From the fact that the compiler of the Haggadah connected these words to the story of the Sages who were reclining and recounting the Exodus from Egypt all night, it implies that they continued to tell the story of the Exodus even after eating, when they were already fulfilling their obligation to recount the Exodus, as the story continued until the morning Shema recitation.

2. As it is brought in the Talmud (Pesachim 109a), one should hurry to eat the matzah on the nights of Passover, as explained by Rashi, Rashbam, and the Rambam, meaning that one should hasten to eat. This is the ruling followed by the Shulchan Aruch (Orach Chayim 486:1). Therefore, it is found that before the meal, the recounting is shortened, and the recounting that is praised is the one that comes after the meal.