The Spell Does What it Says:
For the duration, you sense the presence of magic within 30 feet of you.
So you know:
"Wait, magic is nearby . . ." (Jeremy Crawford Tweet: https://twitter.com/JeremyECrawford/status/803821339412955136)
If you sense magic in this way, you can use your action to see a faint aura around any visible creature or object in the area that bears magic, and you learn its school of magic, if any.
"I'd like to use my action to see what it is I feel," which would reveal the aura of any visible magical creatures or objects in the area. This says all 10 would glow with the aura of their particular school of magic.
Regarding Sigular/Plural Wording Problem
This isn't a unique issue to Detect Magic, Detect Evil and Good has a simliar wording issue:
you know if there is an aberration, (etc.) within 30 feet of you, as well as where the creature is located
Discussed here: How many things can Detect Evil and Good detect at once?
In both cases, if it was singular was to mean one object/creature, it isn't clear WHICH one to pick, and historically both spells revealed all objects/creatures. The presence of "any" in the Detect Magic serves to drive the point home. I'm still looking to see if I can find Jeremy describing the use of the spell with multipule magical sources.
The singular 'its' refers back to the (single) aura that each specific source has: "If you sense magic, you can use your action to see a faint aura around any[thing] in the area that bears magic, and you learn [each aura's] school of magic, if any."