O que exatamente acontece na hora?

Isso foi respondido pelo próprio Peter no filme:

Peter: Do you remember when we were in space? And I got all dusty? I must've passed out, 'cause I woke up, and you were gone.

Peter: But Doctor Strange was there, right? He was like, "It's been five years. Come on, they need us!"

E também respondido por AJ em um post semelhante:

As Director Joe Russo explains,

As for Peter Parker and those who got dusted, they were basically taking a nap in which no one ages. "To those dusted people, they had no conscious in these past 5 years," Joe Russo went on. "They didn't know what happened. It's as if they had just woke up from a long sleep. The only one who was aware about how many years has passed was Doctor Strange, because he has already seen that when he was time mediating on Titan.

Também a partir de BGR:

Q: What about those people who got dusted? What did those five years mean to them? Why didn't they grow older when undusted?

A: Yes, those people whom was lucky to survive the snap are 5 years older than the people who just got back. The reason Spider Man saw his friend again in high school at the end was simply because his friends was unfortunately also dusted like Spider Man was. Of course, there are people in his grade whom didn't die and they are probably already in colleges by now. To those dusted people, they had no conscious in these past 5 years. They didn't know what happened. It's as if they had just woke up from a long sleep. The only one who was aware about how many years has passed was Doctor Strange, because he has already seen that when he was time mediating on Titan. Parker's reunion with Ned was a touching moment. There are also people whom indeed moved on but suddenly was reunited with their lost ones. Yeah it's kind a complicated world now.

I was confused because if it just returns the missing people, why does no one seem to age? When Peter Parker returns to school, everyone is still the same age as he was but theoretically, they should be 5 years older.

As pessoas que estavam bateu acabaram de ser trazidos de volta (para os anos 5 mais tarde) e o restante da população viveu esses anos.

É verdade que parece haver alguma discrepância entre as idades, mas não sabemos quem foi fotografado e quem não esteve na montagem, portanto, é possível que aqueles que do ver também foram quebrados.

As criaturas vivas são trazidas de volta ao presente, o tempo não é redefinido e aqueles que sobreviveram não são redefinidos para cinco anos atrás. Sabemos disso porque é isso que eles tentaram fazer, e Tony pediu que eles fizessem. Também sabemos que os que sobreviveram ainda são os anos 5 mais velhos, pois Cassie não voltou mais jovem. Também sabemos que aqueles que foram trazidos de volta parecem ter a mesma idade que vemos com Peter, que ainda está na escola, e comenta algo no mesmo instante em que ele estava sendo apagado e no seguinte estava de volta.

Peter Parker sentiu que não havia passado nenhum tempo, então presumivelmente as pessoas quebradas não envelheceram.