Timing when you leave the house/office to catch the bus matters a lot more when weather is miserable and/or when buses arrive infrequently than when they arrive frequently and the weather is nice.
The bus I take most often is scheduled to run every 3 minutes on average during my morning commute. That means that even with severe bunching I rarely have to wait more than 10 minutes. Unless it's under 10F outside or is raining buckets, I just leave the house when I'm ready to leave the house, and use the bus predictions mostly as a way to manage frustration levels.
It takes me about 90 seconds to get from home to the bus stop if I make the light, BUT there's a really long traffic light in between. If the bus is listed as 4 minutes away, I have a 50% chance of catching it (depending on whether it makes the previous light). Less than that and there's a 90% chance I'll miss it.
Also, the arrival predictions seem to be based on distance and stop count rather than typical local traffic conditions. It also doesn't take into account times when the bus is empty and skips most stops or is full and not only stops everywhere but boarding and debarking take forever. Which means that while it's eerily accurate for certain stops and times of day, at others I can count on the bus to arrive in half the time predicted and at yet others in twice the time. Unless there's a crash or construction along the route, in which case all bets are off.
During my evening commute, the buses are scheduled much further apart (and are a much longer walk from the office). A 10 or 15 min scheduled headway means leaving whenever you're ready works well if the buses are reasonably spaced (regardless of whether they're actually on schedule). But bunching sometimes causes a 20-25 minute wait (and occasionally more). What I find the bus arrival predictions best for is to be informed on those occasions when the bus is half an hour away and your best bet is to say "screw it" and walk or take a cab.
On another route I frequent, I get on at the first stop on the line. The next bus is always parked around the corner (unless it's super late completing the incoming leg of the route). The app I use lists it as due in 1 or 0 minutes. The actual arrival time will in fact be the scheduled time.
What it comes down to is mostly about knowing your route and adjusting your perception of the predictions to take that into account.
The article suggests people will use these predictions to spend more time at home before leaving their bus stop. If that is the case, what happens if the prediction says their bus will be, say, 10 minutes later, but then that bus catches some lucky breaks with lights, heavy traffic unexpectedly clears up, etc., and the bus makes up 5 minutes of that?
People who relied on the prediction could miss their bus.
Is there a mechanism to address this?
The only one that I can think of offhand that would cover almost all cases would be if the predicted arrival times are also sent to the buses, and if the buses arrive ahead of the prediction they wait until the predicted time before leaving.
You wouldn't want to do that for all predictions, though. Maybe only predictions made within 10 minutes of the original scheduled arrival time are binding, or maybe only predictions made when the bus is within three stops of the stop in questions, or something like that.