No it does not. You may be confusing paraphenylenediamine with BBDE or Butanediol Diglycidyl, which is a chemical that is used to enhance the cross-linking of the hyaluronic acid in Restylane and Juvederm. The two are not related.
It sounds like you might be allergic to hair dyes, since people who are allergic to paraphenylenediamine usually are allergic to permanent hair dyes or the dyes in furs (forgive me PETA for even mentioning furs!). If you are significantly allergic to PPD you should also avoid sulfa drugs, be careful with antidiabetes drugs related to sulfonylurea, Benzocaine ( used frequently, including in our office as a topical anesthetic), Procaine ( an injectable anesthetic) and PABA sunscreens.
You should also be aware that PPD can cross react to color film developer (is this used anymore?), epoxy resin (a hardener) stamp ink pads, and black rubber products.
However, fortunately, you should be fine with Restylane and Juvederm.