For the black guy on the black background: your metering will see very little light coming from your scene, so the camera will basically over-expose. The solution here is to use exposure correction (-1 EV to start?), or go manual and use a gray card to determine your exposure.

For the black shorts on a magenta background: on automatic white balance, the camera will try to get an overall neutral colour. It sees that heavy magenta background, with no other colour, so it will push the colour towards blue/green. Adjusting the colour temperature of your jpeg from 6500K/tint:1 to 7500K/tint:0.98 gets rid of the blue cast. That gives a bit of magenta in the upper right part of the shorts, but that's a normal reflection of the background.

White balance errors aren't much of an issue when shooting raw (as the whitebalance isn't applied to the raw data), shooting jpeg you have to be a lot more careful. So either set a custom white balance on a test target, or set a fixed white balance (depending on your light source). If you are using any kind of led or fluorescent light, the white balance target is the best solution.