The Spidey series is apparently both part of the 616 universe and contemporary, despite the continuity issues created by that decision.
Asked about a "Spidey" book teased at a retailer presentation during the convention, Director of Content and Character Development Sana Amanat disclosed that it's an all-ages series about Spider-Man in high school, written by Robbie Thompson.
"It's called 'Spidey,'" Thompson said. "It's an all-ages book. When Nick [Lowe] called me up about this, I was so, so excited. I think the tagline is, 'Before He was Amazing, He Was Spectacular.' This is Peter Parker as a teenager. They're all standalone stories. These are designed to be in the classic Marvel mold; every issue is a first issue. I think we all have this memory of Peter being in high school for like seven decades, but it actually wasn't that long. These are those stories." Thompson likened it to '90s series "Untold Tales of Spider-Man."
The fan asked if the series took place in the mainstream Marvel continuity. "I believe so," Amanat answered. Editor-in-Chief Axel Alonso said that Marvel has responded to a demand for more all-ages content, and called the series "entry-level" Spider-Man stories that are "for everybody." He also stressed the importance of the series being contemporary, not "creaky and cobweb-y."
Today, he’s the world’s greatest super hero. But long before he swung from rooftops as the Amazing Spider-Man, he was just a spider-powered teenager who knew that “with great power must also come great responsibility.” Today, Marvel is pleased to announce SPIDEY #1 – a brand-new ongoing series launching as part of All-New, All-Different Marvel! Follow the adventures of teenaged Peter Parker in a new series set within continuity from rising star writer Robbie Thompson (TV’s Supernatural, Silk) and blockbuster Marvel Young Gun artist Nick Bradshaw (Wolverine and the X-Men, Guardians of the Galaxy)!
In the end, try not to overthink it. Spiderman has aged less than 20 years in over 50 real-life ones, so time has always been weird for him.