Three possible candidates seem to exist for the first verified (non-participant) observation of a torpedo boat assault. The options are the Russo-Turkish War, at Caldera Bay, or at Weihaiwei, all of which I've described below in the detail I have. I am leaning towards Weihaiwei as there is a report of British, American, French, and Russian observers at the battle, but Caldera Bay was witnessed—to a degree at least—by a British cruiser. Where from, and in what way, did the first detailed account of the use of self-propelled torpedoes reach the Royal Navy and the United States Navy?
Note I've used 'detailed account' as something that would have been useful to the two navies (the USN because it was the next one to go to war in the Spanish-American War), not just a newspaper snippet that wouldn't have given the military much detail (unless we've got post-war reports of say the Russian or Chilean officers going to the other countries to describe their experience?).
Wikipedia says that the first use self-propelled torpedoes in combat was the sinking of the İntibâh by Captain Makarov's torpedos in the Russo-Turkish War of 1877–78. Makarov was in command of Velikiy Knyaz Konstantin, a torpedo boat tender that had four torpedo boats, and these were involved in the operation on 16 January 1878 (unsourced). However, this account is questioned:
According to some sources, the first use of a locomative torpedo to sink a ship in combat actually took place four months before the Battle of of Pacocha, on the night of 16 January 1877, when Russian torpedo boats operating in the Black Sea under the command of Captain Stepan Osipovich Makarov sank the Turkish Intibah. These accounts give little more detail than that. They state that a pair of torpedo boats carrying Whitehead-type torpedoes, along with possibly two others mounting spar torpedoes, attacked and sank the Turkish vessel. There is only one problem with this account: it most likely never happened, at least, not at all as that bare outline would have us believe. To begin with, it is unlikely that the incident took place on 16 January 1877, as war was not declared between Russia and Turkey until 24 April of that year. Secondly, it appears that whenever the attack took place, the Turkish ship that was the target almost certainly was not named Intibah, as that name appears in no contemporary lists of Turkish warships. Third and most seriously, whatever Turkish ship was attacked, it almost certainly did not sink.
... the excited commander of the Russian torpedo boat reported the sinking of his intended target; this claim was never questioned and became a standard component of Russian naval history.
—Stem 'Destroyer Battles'
Based on this, it is relatively clear there was no non-Russian verification of the success of torpedoes in that battle—unless it can be disproven?
The next combat instance seems to have been the sinking of Blanco Encalada at Caldera Bay in 23 April 1891. The armoured frigate was against two torpedo boats; Wikipedia says that it took five torpedoes to sink Blanco Encalada; Stem (in the same book as above) says it took eight and he concludes the account of this battle:
At dawn they [the two torpedo boats] ran into the rebel steamer Aconcagua heading towards Caldera with a deck full of troops and were about to attack when a cruiser was seen approaching from the north. Believing it was the rebel Esmeralda, the loyalist torpederas chose discretion and resumed their run to the south. The ship turned out to be HMS Warspite on her way to Caldera to check out rumours of an impending battle. Her captain wrote up an extensive report on the torpedo attack, which was the first word to Europe of the success of this new weapon.
This leaves it uncertain who Warspite based her account of the battle: quite possibly the survivors from Blanco Encalada, but it's not written who saved them. The steamer, meanwhile, doesn't take part of the battle in any way in that account. The main question here is whether the British shared this account with other countries as they seem to have been the only ones in a position to get first-hand accounts: in other words, what does "word to Europe" mean.
The next use of torpedoes seems to have been at Weihaiwei on February 5 1895 by ten Japanese torpedo boats (unsure about the number of torpedoes on the first day), and hit Dingyuan which was taken out of action. Three torpedo boats returned the next night and launched seven torpedoes, sinking Laiyuan, Weiyuan, and Baofa. Stem mentions this only in brief (and only Dingyuan, not the other vessels), but it is described elsewhere:
... Warships from around the world crowded into these narrow waters to witness the world’s first torpedo battle. Britain alone sent four; the United States had three anchored in the Bohai Gulf, France and Russia one each.
The boats slipped between the booms and entered the harbor, but in the darkness became separated and wandered about. Eventually, each one came upon an enemy ship and launched its torpedoes, but in some cases the powder was damp, and the torpedoes failed to detonate. Friendly boats collided or got stuck on reefs on the way back. Meanwhile, the enemy began to open fire, causing the sea to get rough, but fortunately none of the boats went under. They fumbled their way around the harbor and then returned to base with no indication that the intended results had been achieved. ...
Later, however, a startling discovery was made. The Dingyuan, the enemy’s strongest warship and Ding’s flagship, had been severely damaged in the torpedo attack.
—Shiba, 'Clouds Above the Hill, Vol. 1'
This suggests that an independent verification of the use of torpedoes came from the Battle of Weihaiwei, unless of course as noted above the British actually shared whatever results with everyone equally.