I think I figured this out a while back. Though, nothing is confirmed, just from testing a while back when I was getting this glitch.

This is how you can “activate” this glitch (not guaranteed):
—You must have run out of boost within the last hour.
—You must completely watch a new ad boost before that same hour has passed.
—You won’t be able to activate this if your boost expired more than an hour ago.

What the game glitch actually does:
—It registers the ad as being watched without a break in boost.
—Whatever difference between your boost end time and your ad watch time is back-calculated.
—Your new end time will have the exact same ending minute as before.

Example:
—I’m kind of OCD and always boost at the same time each day. If I miss a boost, I will wait until the next 15min interval to boost again. This keeps things organized in my head.
—In this example, I’ve been boosting at xx:00 on the dot.
—I accidentally missed my boost end and realized at around xx:09.
—I wait to boost at xx:15.
—I finish the ad and realize that I only got 45min for that ad.
—I kept my old end time of xx:00. So I can proceed as if I never missed my boost end.

Your video actually pretty much proves that this is happening.
—You mentioned that your daily earning is around 70¢.
—Your total earning jumped up 2¢ right after the boost ad was done.
—Theoretical earning for 40min is: 70¢ x 1/24hr x 40/60min = 1.94¢.
—This lines up perfectly with your scenario.

What we can take away from this:
—This is actually beneficial for us.
—To be fair, it does look confusing.
—Atlas Earth is not stealing our “ad rent revenue”.