Front or back focus issues can be the result of any of several issues. It's usually a combination of more than one of them since there's no such thing as a perfectly aligned lens, mounting flange, and focus system.
The focus elements in the lens not moving exactly as the camera instructed is only one such cause. That particular issue most often results in inconsistent focus from shot-to-shot, rather than a consistent front or back focus. In a series of several shots a few will be slightly front-focused, a few will be slightly back-focused, and a few will be somewhere in between. Please see this excellent blog post written by lens guru and lensrentals.com founder Roger Cicalla. Although he bases the discussion on several Canon bodies used with the same lens, the methodology he uses and the things he finds are applicable to AF systems in general.
When a system consistently front focuses or back focuses another possible cause of the problem is that the distance from the lens to the image sensor is not the same as the distance to the AF array via the secondary mirror. This is probably what is happening with your manual lens. It's very similar to when the optical path from the lens to the camera's view screen/focusing screen is a slightly different length than the optical path from the lens to the sensor (or film). If things are perfectly focused in the viewfinder then the image projected on the sensor is slightly off on one direction or another.
In addition to the possibility that the flange distance to the AF sensor array and the sensor are not exactly the same there is also the possibility that the lens is slightly too far forward or back for the correct flange focal distance of the camera. Differences as small as 20 microns (0.000787402 inch) can be measured on a sophisticated optical test bench.
Without knowing the particulars of your camera and lens models it is difficult to advise on how best to deal with the issue. You may need to calibrate the camera's overall AF offset to match the manual lens, then adjust the camera's individual lens AF offset for each of the AF lenses you own.