A vibrating sensation in the testicles can be caused by inflammation of the prostate gland. The pain or sensitivity from it can be referred to the testicles.
Causes of this inflammation can be infection, sitting for long periods of time, exercise that is too vigorous and exposes the area to great stress, such as horseback riding, or too much intake of caffeine, alcohol, or spicy foods.
If there is infection, it can back up into the male urinary tract and cause more referred pain as well.
It is best to see your doctor to rule out any possible infection if these symptoms persist, so that you can get treatment before any further complications should arise.
In the meantime, when sitting for long periods, get up and take breaks occasionally, and use some cushioning for the seat to protect the testicles.
Good luck and I hope this is helpful.