They didn't, the Romans did. The lambs were killed on the 14th. The 1st of unleavened is the 15th...
In the first month, on the fourteenth day of the month at even, ye shall eat unleavened bread, until the one and twentieth day of the month at even...
In the fourteenth day of the first month at even is the Lord’s passover. And on the fifteenth day of the same month is the feast of unleavened bread unto the Lord: seven days ye must eat unleavened bread. In the first day (of unleavened, the 15th) ye shall have an holy convocation: ye shall do no servile work therein. But ye shall offer an offering made by fire unto the Lord seven days: in the seventh day is an holy convocation: ye shall do no servile work therein.
And there shall be no leavened bread seen with thee in all thy coast seven days; neither shall there any thing of the flesh, which thou sacrificedst the first day at even, remain all night until the morning. Thou mayest not sacrifice the passover within any of thy gates, which the Lord thy God giveth thee: but at the place which the Lord thy God shall choose to place his name in, there thou shalt sacrifice the passover at even, at the going down of the sun, at the season that thou camest forth out of Egypt. And thou shalt roast and eat it in the place which the Lord thy God shall choose: and thou shalt turn in the morning, and go unto thy tents. Six days thou shalt eat unleavened bread: and on the seventh day shall be a solemn assembly to the Lord thy God: thou shalt do no work therein...
And in the fourteenth day of the first month is the passover of the Lord. And in the fifteenth day of this month is the feast: seven days shall unleavened bread be eaten. In the first day shall be an holy convocation; ye shall do no manner of servile work therein...