Alvarez was taken on a stretcher to the pool's medical centre, with teammates and fans appearing to be in shock poolside.
The US swim team later released a statement saying that Alvarez was doing well.
Fuentes, a four-time Olympic medallist, told Spanish radio that Alvarez had fainted due to the effort expended during the routine.
"She only had water in her lungs, once she started breathing again everything was OK," said Fuentes.
"It felt like a whole hour. I said things weren't right, I was shouting at the lifeguards to get into the water, but they didn't catch what I said or they didn't understand.
"She wasn't breathing ... I went as quickly as I could, as if it were an Olympic final."
Fuentes said Alvarez planned to rest Thursday and was still hoping to compete in Friday's team event after further medical checks.
The 25-year-old Alvarez was in her third World Championships. She also reportedly fainted during an Olympic qualifier in Barcelona last year.