It is not a surprise that the FBI (or CIA) investigates or closely monitors an organization. However, I don't understand when they arrest several of FIFA's members, some of whom are not American, in Switzerland. FIFA is based in Switzerland. Shouldn't the Swiss government be involved in the public arrest and trial of FIFA's executives and board members?
Absent international treaties on the matter, every country is free to decide what it has jurisdiction over. That's because jurisdiction just controls what that country's courts do -- American jurisdiction means that American courts are willing to try the person and American law enforcement can arrest them if they set foot in America, and the only time the US doesn't get to establish jurisdiction is if US law prevents it (e.g. the Constitution) or if an international treaty forbids it (e.g. diplomatic immunity).
In this case, the allegations involved the use of US banks, and are heavily focused on the Miami-based CONCACAF. Several companies involved are US companies. US law gives jurisdiction at fairly low levels of connection to the US, and no one else gets a say in the matter. It's the same way in other places; Spain had a judge (Baltasar Garzón) who was (in)famous for making heavy use of their universal jurisdiction laws to investigate human-rights abuses having nothing to do with Spain, but which Spanish law could prosecute.
Of course, the fact that US law gives jurisdiction is only binding on US law enforcement and US courts. US courts can't order Swiss police to make an arrest or send someone to the US, and US police can't go into a Swiss hotel and slap handcuffs on people; for the arrest, there needs to be Swiss involvement (or use of force by the US, like in Panama in 1989; that's not typically the preferred option, though). If the US claimed jurisdiction over a German citizen mugging a French citizen in Poland, Switzerland would basically just laugh at the request (and if US law allowed jurisdiction there, Switzerland wouldn't enter an extradition treaty with the US).
However, in this case people in Switzerland were arrested by the Swiss, who absolutely do have the power to arrest anyone in Switzerland if allowed by Swiss law. Switzerland has agreed to normally extradite people to the US if they're not Swiss and if they're wanted in the US for violating certain kinds of laws by doing something that's also illegal in Switzerland. So, the Swiss (exercising their jurisdiction over anyone in Switzerland) put the people on a flight to the US according to Swiss law. When the flight lands, the people are in the US, and US law enforcement then take them before a US court that only cares about US law.