I have no idea why, exactly, but the 2010 Census shows a population of 3,740 for the block containing the Pre-Trial Detention Facility (Census Tract 10 - Block 2034, bounded by Liberty, Adams, Marsh, & Bay.) The block containing the Community Corrections Center shows a population of 0. It's possible they use the Pre-Trial Detention Center as an address location on the census for inmates at other facilities, but that's just a guess.
Whether shelter populations should be counted, I couldn't say. They are at least free citizens. Plus, they're more or less a staple in most city centers, so they don't skew comparisons quite as much as a massive jail.