No, both paragraphs agree that the procedure is delayed until 1 week before release.
From one paragraph:
According to the law, the process will be carried out by the state's Department of Correction, but it cannot be conducted more than a week before a person's prison sentence ends.
From the next paragraph:
Cascio said, "It has to be done no later than one week prior to his release date, so they could do it immediately or they could wait."
The first says "cannot be conducted more than a week before" and the second says "no later than one week prior" and "they could do it immediately".