How long are your workouts? It takes a while for your body to "get it" so to speak. I wouldn't sweat it, take it easy and pedal at your expected effort for your target zone. Don't worry about the red light. A minute rest here and there won't hurt. Think of it as natural intervals! After warming up properly, your HR will creep upward for the same amount of effort and you'll reach your target easier.
Jeff Galloway, of Gallowalking fame, even advocates walking a minute after each mile of running during a marathon.
Your goal should be the total amount of time spent in the zone. So warmup, ride in your HR zone, stop for a latte, ride home.