Mary Beard's The Roman Triumph says that the date of the triumph is unknown. Pompey is said to have been somewhere between 24 and 26 years old and was not yet in the senate.
Pompey's second triumph was awarded him for his victory in Spain in 71 B.C.
Pompey's third triumph was the one for his eastern victories and was awarded in 61 B.C. It is the best documented of all Roman triumphs, although details of the event seem improbable or even incredible. It was a lavish two-day affair that included, on the parade, a statue of the defeated Mithradates 8-cubits tall and made of solid gold, according to Appian.
As Monroe E. Deutsch says in "Pompey's Three Triumphs" this series of triumphs was impressive not just for its number but for the fact that each victory was on a different continent and by winning in each division of the known world, Pompey had, in a sense, conquered the world.
An additional anecdote from Deutsch, about the importance to Pompey of the triple triumph is that he had representations of the trophies from the 3 triumphs inscribed on his ring. It was this ring that convinced those in Rome that Pompey had indeed been murdered in Egypt.
Source:
"Pompey's Three Triumphs," by Monroe E. Deutsch. Classical Philology, Vol. 19, No. 3. (Jul., 1924), pp. 277-279.

