No...
It would be the Tigers' 3rd rounder. The pick sacrificed isn't the same as the 4th rounder the Padres gained.
It is the Tigers' third pick, but their third pick is actually the competitive balance pick which is ineligible to be forfeited. If, however, they acquire a competitive balance pick in a trade, the acquired pick becomes forfeit eligible and the sacrificed pick would be either that acquired pick or the second rounder depending on which pick is acquired.
That is to say... probably their 3rd rounder, but I wanted to explain the scenario it is another.