It does work in the background on Android, and I gather background scanning is coming on iOS.
As someone above said, don't get the perfect be the enemy of the good. Get it out the door, get it tested while you wait for Apple to get their act together is not only reasonable - it's the by far the best forward as an engineering strategy.
It runs in the background. It logs all encounters by either advertising its presence (Peripheral mode) or scanning for devices (Central Mode). They alternate between these states. When two devices encounters it's logged on both sides. That device is blacklisted for a few cycles to avoid constantly logging it.
The 15 minutes 1.5m conditions are applied on the reporting side after it is uploaded.
No conscious effort. Kinda like how your email client pings you when you receive an email. When was the last time you had to consciously think for an email to come into your mailbox?
If it worked in the background that’s more useful and realistic.