mobile data record time

No. That time stamp is when the usage was reported. Actual usage time could be then or hours to days prior.

I think my daughter is on her phone in the middle of the night, last night at 2:am and then at 4:00 the other night ( early morning) am so I'm wondering how accurate might need to take her phone away

its a reoccuring issue 

as stated before data usage is updated/uploaded at night when your less likely to be using the phone and the data could be from that day to a couple days before 

shes pretty sneaky and has been caught. before I will keep her phone at night from now on.

Thank you I appreciate your help.

Also, it’s usually aggregate data.  It doesn’t mean that exact amount of data was used at that exact time.

Plus a phone will use small amounts of data even if the phone itself is not being used. You may still see those 2 and 4 am usage records even after taking the phone away. Unfortunately, those usage records don’t prove your daughter is using her phone in the middle of the night.