What to do immediately after informing the journal's managing editor that you are withdrawing your paper submission in their journal?
Waiting for them seems like a lost cause. Unless you have signed some release or given them copyright, the paper is yours. You can submit it as you like. 

But submitting it minutes after notifying them of a withdrawal might be hasty. A few days wait is suggested. But they don't seem to have a very good record of corresponding with authors.