"Paying attention to" a person means that you talk with them, listen to them, spend time together, etc.
People are supposed to pay attention to their children and families, so it's usually in this situation that people talk about "paying attention to" people.
There's also another meaning of "paying attention to" someone. This other sense means to look and listen carefully to someone at one certain time. For example, parents might tell their kids:
Pay attention to the teacher!
But the meaning of this is a little different from:
I'm worried that we haven't been paying enough attention to Zack ever since Adele was born.