A blockade here would be similar to the "Distant blockade" concept the RN followed during the Great War; There's no need to loiter off a hostile coastline with your heavy units, when geography dictates where the Peruvians will basically be going, should they chose to go anywhere; To have any real impact, Peru is forced to head north along the coast towards Panama to support attacks or conduct raiding on the Columbian coastline.
While in theory, units of the Peruvian Navy could attempt to either round the Cape, or even try a reverse Graf Spee and go across the Pacific, around Africa, and show up in the Caribbean....but does Peru have the logistics to support that long of a cruise? And even if they do, there are several chokepoints they'd have to traverse and be seen doing so, giving ample warning of the attempt.
Commerce raiding seems less of a concern to me than what I've seen comments about; Unlike the German raiders preying on the copious amounts of British marine traffic around the world, is there enough soley Columbian traffic worldwide to make a distant raiding cruise worthwhile? Assuming the Peruvian loyalists are at all rational, attacking any non-colombian traffic will only bring down the Fist of an Angry God upon them. That means local raiding only, which like any purely military cruise, means sailing north into an area with natural geographic boundries set by the coastlines.
In regards to the Mutiny, I don't view the events as played to be quite that unreasonable. This isn't a replay of Catapult, with the Peruvians being given humiliating terms at the barrel of a gun of what was a few days ago their ally. The eventual terms worked out was for the Peruvian ships to be interned in Iberia, which is a noncombatant in this conflict, as well as an otherwise direct ally of Peru; the Chileans did not demand to take the Peruvian ships back to a Chilean or Lantean port for internment. And to boot, it's strictly stated as a temporary internment pending diplomatic recognition of the Congressional faction in Peru. Rufino's decision is one that takes the endgame as paramount; recognition of the Congressionals as the legitimate government of Peru over the warmongering Presidente. Once this is accomplished, it stands to reason the temporary internment has a better than even chance of being ended, and allowing him to return with his ships and crew to Trujillo with news of inernational recognition and possibly support of the Congressionalist faction, surely a much better endgame than an unwanted and ultimately pointless confrontation with the Chilean and Lantean navies. Rufino may have been able to make a respectable showing in such an engagement, but what would he have accomplished to support the goals of the Congressionalists by doing so? A valiant battle against the enemy would give the President something else to crow about, and deny his forces the ability to further support the Congressionalists.
The concentration of heavy units isn't all that conspicuous; You have the two Battleships at Callao, and Rufino's Destroyer squadron shows up from...somewhere else, and that's essentially what mutinies. The other heavy units are elsewhere; Huascar is sunk, Grau is at another port. There's also a handful of other cruisers either at Callao that didn't participate, or located elsewhere. Regardless, Callao seems to be the Peruvian Navy's home port, so any dispersion would be to ports not neccesarily prepared to support those ships.
I somewhat concur with the rapid ease in which the Chilean and Lantean fleets converged on the Peruvians, but then again the allied Heavy units only have a limited number of targets to keep track and prepare to intercept; Less so with the Huascar's sinking, and the Grau presumably needing a few days to resupply before embarking on another sortie (And as mentioned, possibly at a port not prepared to do so). Assuming the Allied forces are chosing something similar to a Distant Blockade, and/or following a similar model of containment attempted during the Bismarck's OTL breakout, you don't waste your heavy ships doing the close-in patrols. Your other forces locate the target, and direct in the heavy units. In this case, finding the targets is all that much easier with Rufino's continual radio broadcasts to triangulate on.
You're right that the entire allied fleets would not likely be at sea at the same time, but this event does occur only a few days after the sinking of Huascar, and only a day (or less) after the Grau was spotted by the Argentinians (ergo, the Allies may or may not know she's put back into port yet, and be deployed in attempt to intercept her)