Is using epoxy this way on a kitchen sink installation/repair acceptable?
Considering you are having a problem and this unit was installed professionally and has a warranty on it. Call them back out to fix the thing right . If it had screws to retain it and one broke off on installation and now they need to fix it - too bad for them - they should fix it - why should you have to live with a problem or potential problems - you probably worked hard for your money - depends on how much you value what you paid for.  

What I am guessing (from my experience) is that there was a mounting screw attached to the sink that held it in place and the screw popped off the sink itself - of course there could have been a metal piece attached to the quartz as well usually with an epoxy.


  What does the other mount side look like a picture of that would
  make it easier for people to know exactly what you are talking about. There should be at least 2 mounts if not 4.


I would call them back and say hey I have a problem and I thought to go fix it myself but this is what I found .. I want the thing fixed and fixed right. Where fixed right means you should not have a problem with it - especially with in one year! 

EDIT 11/15/2017 
Using your posted picture I wanted to outline something I noticed .. notice the ring outline near the repair - in your second photo with a correct mount shown you can see the metal ring - in the first photo you posted you see an outline where something was but it is gone - I am thinking the fish docks are wafting some air - smells fishy to me.