Short answer: No, thanks, this is not necessary.
Since dblp indexes the tables of contents of complete proceedings or journal volumes in bulk, your latest publications will be added to dblp as soon as we process the containing volume. So there is no action on your end necessary to have your papers added to dblp.
This is particularly true for your "Online First" publications. Please read how dblp handles Online First publications here.
Due to our huge backlog, processing of newly published issues or volumes may very well take up to several months until we have the resources ready. However, there may also be cases where the publication of a volume or issue goes unnoticed by dblp. So if you notice that a new volume or issue of a journal or conference series indexed by dblp has not been added for, say, more than a year, a gentle reminder is of course welcome.
If a relevant computer science journal or conference series is not yet indexed by dblp, you may of course always suggest the series for indexation.