Short answer: Bill Clinton’s policies contributed to maintaining and increasing mass incarceration, but they affected Whites more than Blacks. Edit to short answer: Over in my full post on my own blog, I added graphs of the federal system, where Black imprisonment did go up under Clinton more than White imprisonment did. Federal system is smaller than state systems, so the overall patterns are dominated by state systems. The full post also gives graphs for other races.
The vertical line at 1995 represents the first year Clinton’s crime bill could take effect. Black state imprisonment leveled off during the Clinton years while White imprisonment continued to rise steeply. The Black/White disparity declined in the Clinton years. The steep rise in the Black imprisonment rate occurred during the Reagan/Bush years and the drug war, which was at its peak in the late 1980s and early 1990s, before Clinton took office.
More details and data sources over at my academic blog Race, Politics, Justice.