Can I use text from my dissertation in a manuscript?
In general this is OK or, in some fields, even recommended. It does not make any difference if the dissertation comes first and then the publication or vice versa.

However, I would reference the thesis/paper(something along the line: this paper was part of my dissertation ... or this chapter was published as ...) and you should talk to someone (your supervisor? the postgrad coordinator?) in your department about that. There might be some rules regarding that practice (I never heard of anything like that but just to be on the safe side).

Btw: Self-plagarism has nothing to do with copyright violations.