The definition for joint custody is whatever the parents/courts make it in specific cases. Some parents have joint physical custody but still only get their children 3 days a week. For others it’s equal time. Joint physical custody is whatever is spelled out in the agreement or order.
As far as the definition for well-being, that means that if there is something going on with the child you must inform the other parent. This does not mean that the other parent needs to know where your new boyfriend/girlfriend works or lives. This is not directly related to the child. It does not mean that the other parent needs to know every detail about your days and every interaction that the child has while in your care. It only means that you must keep that parent informed if the child is sick, or if there are major issues that have long term affects, academic progress, if the child wants to take up an afterschool activity that may interfere with the other parents time. These are all things that should be discussed and normally agreed on. If you share custody then you should include the other parent on things that are directly related to the child.
The other parent can demand any information that they choose, it’s up to you to determine if that information is needed. If you do not believe that the information being asked is necessary for the other parent to do their part in raising the child, then do not give it. You take care of the child while they are with you and expect the other parent to do the same. You have to trust that the other parent is doing their best. That is the only way that joint custody will work. If the child is being fed, getting sleep, getting help with homework and/or life issues, being clothed, then those are the day to day activities that make up custody. You physically and emotionally care for that child during your custodial time. The other parent does the same. If any of that is not being done, then the other parent has the right, with joint custody, to step in and question that.
Hopefully some of the others have some input also…