The nanny doesn't appear to live in so just assume she had set scheduled hours during the day and went home at night.
So, imagine the scenario where mom was supposed to be in the city for doctors appts during the day (11am and 1 pm if I recall correctly) and Mom doesn't show up at the end of the day?
Further my bet is that mom and nanny are typically texting on an ongoing basis during the day and that day for whatever reason the nanny didn't get any check in texts from mom--this brings up her awareness as this might be unusual for JD.
So, nanny probably hadn't had contact with Mom for most of the day, might have gotten calls from the doctors offices looking for JD as she hadn't shown up for appts and so what does Nanny most likely do?
Its the end of the school day and the kids need to be picked up so she picks them up (she could have been tasked with picking them up anyway that day as JD had a 1pm dr appt in the city which might have meant she might not have been back until after children needed to be picked up. This is an assumption on my part based on travel time).
So, now nanny has the children but its time to go home from work in a little while and yet there is still no mom and mom can't be reached by phone.