There is one more step necessary. As you have removed the album for the person from "People", their album is living in Limbo. You can still search for the name of the person, but the album is not shown in People.
While viewing a photo of the person and viewing the Info - after tapping the tiny button with the miniature face of the person, the hidden album of this person will open. Now tap the three dots in the upper right corner of the album for the person and use the second entry in the menu "Add ... to People". This will unhide the album of this person and add it back to "People" or "People and Pets" depending on your system version.