Two concurrent different versions of a paper to journal and conference; do I need to paraphrase?
As Alexandros says, first you need to make certain that the journal you are submitting to allows content reuse by the typical guidelines, as not all journals do, even in CS.

Assuming that is the case, the typical custom is to wait until your shorter paper is accepted to a conference, though it doesn't matter if acceptance has been announced to anybody besides you and the conference program chairs.  There is nothing hard and fast about this custom, however, since your manuscript will be separately reviewed by the journal to its own standards.  Confirm with the editor that it's OK before submitting and clearly disclose the situation in the cover letter so the reviewers will know as well.

If you do this, however, you are taking a risk, because your submission to the conference may not be accepted.  If your paper is rejected then you probably cannot submit to another conference.  This is because the new submission would now be a subset of a paper under review, not an extension.  You might thus end up with a piece of work that stays in limbo for much longer than usual (CS journals often don't have much sense of urgency, because of the existence of conferences).  You need to decide whether you are comfortable with taking that risk.