There are two danger periods: passing through the galactic plane (duration 100k years every 35Myr) and passing through the galactic arms (duration 10Myr every 120Myr). The article only discusses passage through the arms.

We're currently moving away from the galactic plane, which our solar system last crossed 3Myr ago.

According to the article there are 11 extinction events spread across the last 500Myr, which corresponds to two orbits of our solar system around the galaxy but one traversal through the arms and spur (they're also orbiting, more slowly). Right now we're in the Orion Spur; the authors seem to attribute an extinction phase near the last exit from this spur; the spur is 1 kly across, so I estimate our solar system takes 3 Myr to transit the width of the spur.

I think our next destination is the Perseus Arm, 6.5 kly away, so we should reach it in about 20 Myr.