This is a pretty simple one. If you’re appointing someone to do something that you’re normally responsible for, you don’t just explain that to them. You need to explain it to everyone else too.
If you’ve asked someone to organise a weekend away, you have to tell everyone that they’re doing it on your authority and they they are the organiser.
If you’ve asked someone to take over the kids program, you have to tell the parents that they are the go-to person if they have questions.
Otherwise, people will assume you haven’t appointed them, and they’ll just keep going back to you.