Thanks all for the answers!
I had myself checked for inguinal hernia a few months ago and the doctor didn't find anything.
I can reproduce the same phenomenon by just taking a very deep breath, bracing and then releasing the breath (i.e. the same thing I do during lifting)
It's good to hear that other people have experienced something similar, I'll have it checked by a urologist then.
That part sounds like an inguinal hernia to me. Update us in a few months on if it was a difficult to diagnose hernia or not.
We are having a large number of testicle discussions here lately. I will be much more in tune with my testicular functioning during this week's lifts.