The Alsietine Water: Not as Healthy as The Romans Had Hoped
So it was this writing from Marliani that caused later writers to connect the erection of the fountain with Pope Hadrian, who had actually only reinstalled the Alsientene aqueduct. The problem, which is more important than who installed the fountain, was that the Alsietine water was unhealthy and unfit to drink.
The writer, Frontino, handed down some of the most important works on the aqueducts, fountain, and all things water, regarding the Aqua Alsietina as follows:
"I do not understand what reason Augustus, a prince as prudent as any other, would have had to bring in Aqua Alsietina (known as Aqua Augusta); the water is not at all pleasing, but decidedly unhealthy and therefore is not used by the people wherever it flows. Unless, when he [Augustus] undertook the building of his Naumachia he did not wish to reduce the supply of any of the more salubrious waters and thus had special conduits made for this water, and then allowed the surplus from the Naumachia to be used for the irrigation of nearby gardens. As a matter of fact, every time the bridges have to be repaired and the aqueducts that cross from the other bank [of the Tiber] are interrupted, it has become usual, owing to necessity, to maintain the flow to the public fountains".
So we know that Maliani saw the ancient aqueduct carry water from the naumachia to the fountain underground. We also know from Frontino that it is also this water, which was unhealthy, that supplied the nearby fountains. So the fountain did exist before Hadrian, who had it restored.