It's really age dependent. We didn't do it as structured as OP going back at exactly 3 minutes etc. When she was under 1 year old she would sleep within 5 minutes, so no need to go back.
Now that she's older and speaking, she sometimes doesn't want to go to bed and will tell you. Then it helps to communicate that you'll be back and they're not on their own. Gives enough comfort that I almost never do more than come back once after 10 minutes or so, and over half the time she's already sleeping. If not I just say good night again, hand back the stuffed animal that by that point has usually been thrown out of the bed and that's it.
Now that she's older and speaking, she sometimes doesn't want to go to bed and will tell you. Then it helps to communicate that you'll be back and they're not on their own. Gives enough comfort that I almost never do more than come back once after 10 minutes or so, and over half the time she's already sleeping. If not I just say good night again, hand back the stuffed animal that by that point has usually been thrown out of the bed and that's it.