Scheduling Question

I have several of the wi-fi bulbs and have a schedule for each one to turn on/off at certain times. My question is, does my app, or phone as it is, have to be here at home, on the same wi-fi for the times to work? is the schedule for each bulb stored in the bulbs, or only in the app?
One more comment. On the rules page, I have several rules for several bulbs. Hard to tell when rule is for which bulb. It would be nice for each rule to indicate which bulb it is assigned to. Just a thought.

The schedules are stored in the cloud and don’t require your phone. Other than to create or modify them of course.

As far as naming rules, there is an optional name field that you can use to identify each rule.