What program can display PDF tooltips on a Linux system?
As far as I know, the only linux pdf viewer that can display tooltips is the linux version of Adobe reader.
Nowadays (2020), there are rather more options for viewing (and adding) PDF annotations for free on Linux. Ones I have used personally include Chromium's PDF viewer, which can display PDF annotations, and MuPDF, which can also create annotations.
Edit: Chromium isn't very good at displaying annotations, and can't display all kinds of annotations, but MuPDF seems much better at it. Also, Adobe Reader is no longer available supported for Linux.
Edit 2: Another option I've tried now is Okular, KDE's PDF reader, which is free (of course) and can create annotations. Its graphical user interface is much less minimal than MuPDF's, but it feels sluggish to me and doesn't seem to support as many types of annotations as MuPDF (in particular, I see no option to attach a file to a PDF document).