We can see that there is a theme running through these two occasions. All of this was done according to the king's command, because "he made all that were found." These Passovers were dramatic changes from the original commands of God given in Exodus 12, in Numbers 9 specifically, and in Leviticus 23. The Bible presents the king as being the driving force in these reforms. These acts that are listed here in regard to Passover were personally supervised by the king so that they would not revert back to their paganism. Apparently it was the only way that they would hew even close to God's original command.
We thus also saw, especially in Josiah's observance, a multitude of other sacrifices from flocks and herds accompanying the Passover-lamb sacrifice. These were the burnt, the peace, and thank offerings normally offered during the Days of Unleavened Bread. Remember that.
These were administrative decisions made during an unusual circumstance by strong and righteous kings. I have no doubt from other verses within these chapters that God acknowledged and accepted these Temple-centered Passovers even though it was against His original intent and His original commands. This acceptance of these Passovers does not by any stretch of the imagination mean that God was replacing a beginning of the 14th sacrifice of the Passover with a Temple-centered late 14th sacrifice, and a 15th eating of the Passover lamb. It is important that you understand this.
Nowhere in these chapters, with these unusual Passover observances, does God give any implication at all of anything other than acceptance of these unusual occurrences. There was no command for His people to change anything that He originally instituted.