How to ask someone to be cited in their paper?
Citations are mostly to establish and credit where ideas came from rather than to establish priority. Simultaneous or independent discoveries are fairly common.

It's appropriate to contact the other authors and let them know about your work. Be polite and friendly, you don't need to accuse and shouldn't request anything.

The script would be something like:


  Dr. PurpleElephant,
  I saw your recent publication in the Journal of Pachyderm Studies and thought you would be interested in our similar work last year published in Colorful Mammals (citation/DOI link). It looks like you found a more general case of ours...


And add whatever pleasantries or commentary is appropriate (for example, if you liked some aspects of their approach, or you want to point out something unique in yours). Hopefully you'll get a friendly letter back, maybe they'll be sorry they missed your work.

Note that this will almost certainly not get you cited in their current work which is already published (possibly it would be different for a preprint), but if they refer to their paper in the future they may also refer to yours. In case of some truly substantial simultaneous discovery, some other venue might be appropriate to draw attention to it, but that doesn't seem to be the case here: sometimes we end up on similar perches from standing on the shoulders of the same giants.