You're secondary might be okay as is, but you can better center it if you want. It's part of the collimation process, but the secondary placement is not axial collimation. Rather it's field illumination as the secondary captures the full converging light cone and sends it up the focuser. Secondary tilt (not its position) aligns the focuser axis to the primary center. You only have a slight rotation "error" as evidenced by the reflection of dark secondary shadow budging toward about 3:30. You can still achieve very good axial collimation.
I understood your question is about axial alignment. For that we need to see the primary center mark (hopefully in better focus) to be under the cross hairs. The cross hair and the Cheshire pupil define the focuser axis. They need to point to the primary center mark, but your image above looks a little off. You're camera lens might not have been centered on the Cheshire pupil, so there may be some parallax error. Since we cannot see the primary center mark, I can't say much about your primary mirror's axial alignment. I do understand sometimes the camera has a mind of its own, but maybe shining some light down the tube will allow the camera to focus better on the primary center and the reflection of the Cheshire ring.
BTW, a Cheshire with cross hairs is called a combo tool, it's a combination of a Cheshire for primary alignment and a site tube for secondary placement and tilt alignment. It looks like you covered the primary reflection in your bottom image, and people do it to ignore all those confusing reflections. But, really, you wanna see those reflections at some point during axial collimation. It's helpful to see them during secondary rotation and refining your collimation at the apex, too. One place a white piece of paper is helpful is on the tube wall behind the secondary and opposite the focuser. It's helps us better see the secondary position. But, for axial collimation, we need to see the primary center mark.