if it is the same data, but you put it in another style for your PhD thesis and created a new figure - does it still counts like "figure from publication "***" ?
The copyright attaches to the "presentation" of the data, not the data itself. If you want to replace (say) barplots from your first publication with the violin plots you used in the rest of your projects, go for it! The publisher doesn't need to be involved.
However, you should still cite the original paper by including something like "data from XYZ et al. (2015)" or "redrawn from " in the caption. This ensures that the reader knows where the original data comes from and avoids implying that those results were somehow confirmed--exactly--by a second set of experiments. More practically, it also means your examiners won't ask for as many changes since the data have already been vetted by the papers' reviewers.
There might be two parts to this question here, so I will answer them separately.
Is it plagiarism if I do not cite my own published results?
Answer: Yes, that's called self-plagiarism. It does not matter if the results you want to cite where published by yourself or another person. It must be cited. Even if you have the same data and plot it differently, it is essentially not a new source. Since you usually have more data accessible from your own publications, you might come into temptation to use an altered figure from a previous publication. These must also be cited as part of the published paper. Better safe than sorry, just cite it if it can be attributed to a previous piece of research.
Do I have the right to reprint figures from a publication in my thesis?
Answer: Well, that depends on which licensing agreement your published paper falls under. For example, the very popular open access CC-BY license allows you to retain the rights to your images and to reprint them. However, attribution (i.e. via citation) must still be specified.
If you do not own the rights to reprint the pictures as they are, you can always redraw a figure (as suggested by Oleg Lobachev in the comments) and correctly cite the source as "Redrawn from Author et al. " or similar.
TL;DR Yes, if you rearrange data from an old publication in a new form you still have to cite the old publication.