IIRC (and it was some time ago), the kernel on the Synology boxes isn't exactly cutting-edge, so you get into problems with newer tuners unless you can compile your own V4L to bring it up to date. In practical terms, that means older DVB-T sticks work well, DVB-S less likely, DVB-T2 less so and DVB-S2 are even more of a challenge. Last time I looked, you needed to use Video Station (Video Centre?) to load the stick, and Synology were only supporting DVB-T on that anyway.
So, unless someone can contradict me with "I have this, it works!", you may need to do some more homework to find what's installed on the box and how you can modify it.