They are also self-managing, meaning they internally decide who does what, when, and how.
So, does Srum (sic) really let people self-organize around their work?
In my experience, the quote you mention is spot on: a self-organizing team can be a great experience for all involved, and produce outstanding results, with long-term hapiness of the members as a welcome side effect.
The big misunderstanding is that we can never expect every single individual to be self-managing, in my experience. The team is self-organizing; not necessarily every single member of it.
The big spiel is that in Scrum and other Agile methods you skip the classical project lead who goes around and - as a non-technical person - tells every single person exactly what, when and how to work. The role of the project lead gets diffused into the team itself.
How this, then, works in practice depends on each individual team. Some teams consist of a bunch of highly motivated and skilled (in the area of time- and self-management) people; and in that case every single person might indeed self-manage.
In other teams I have been in, there were people who simply were not able to do so on their own, but that was fine. They needed "impulses", or they outright needed someone to tell them what to do. But that someone were the other team members, not an external force.
The reaons can be plenty. Someone might just be very fresh and inexperienced; to expect that they magically figure everything out and decide what and when to work would be illusory. Someone might simply not have the motivation or skillset to do so, and in that case they can safely lean back and trust on the "process" (i.e., a Scrum board with readily made, well-refined stories) to guide them what to do, without ever caring a bit about "managing" themselves - they show up to work, work until time's up, and then stop.
Some team members need a mighty kick once in a while; i.e. some people tend to want to "play" all the time, constantly trying out new frameworks, only ever interested in "sexy" stuff, and so on - the classical problem where a project lead would have a 1:1 and probably make them miserable. This job also is transferred to the team. If everybody is trying to make ends meet to somehow finish the work towards the end of the sprint, they might have to reign in one of their own who just is a loose cannon.
The worst nightmare is if a Scrum team has nobody who is capable or willing to self-manage, or cares about what everybody else is doing. Very frustrating experience for all involved. This would be a wrong team setup and need to be addressed like other problems in this area.
So there you have it. TLDR: the team is self-managing, but not necessarily each single team member.