It is possible to have the stock appear to be running true at the rest end, but actually be running off at an angle. The rest will force the work to run "true" when in fact it is off center.
You should sweep the front and the top of the work to make sure it is inline with the axis. use a hammer to adjust the work so it is aligned with the axis.
This will require that you set the work in the steady, and sweep it with an indicator mounted on the carriage while adjusting the steady. Once the steady is adjusted, you will have to remove it temporarily to move the carriage to the right for facing.
If the work is not too heavy, sometimes you can just indicate at the end with the steady open just like you would center work in a 4jaw. When the work is not inline with the axis, it will appear to have two high spots opposite each other, and two low spots 90* from them (it is oval in cross section.
When the work is too long and heavy to be held in the chuck with out support for setting up the steady, you can make a dummy bar. You would turn a stub of the same diameter as the work, and adjust the steady up near the chuck. Then just move the chuck into position for the actual work.
lastly, if the rest is a bit sloppy in the bed, gently twist the base counter clockwise when you tighten it. This will give a bias to the tracking and force the work back into the chuck. Think of the pads or rollers as being a nut and the work as being a threadless screw and it will make sense.