Issues with time limits

I just got this program 2 nights ago & I set it up for my 3 children.  On the first night, my oldest daughter was doing homework & ran out of time.  The program warned her & I was able to give her more time to work on her homework.  Last night, my oldest daughter signed on to this computer before her time curfew.  She did go past her time curfew & signed in 3 or 4 times & was then blocked.  She used the upstairs computer, too.  This morning there were probably a hundred messages saying that she kept trying to sign in every couple of minutes from around 11 pm-3:30 am.  I know that she wasn't up at 3 am.  So tonight when she tried to use the computer, it logged her off because she was out of time for the day.  If the computer was updating Windows or the antivirus program, would it do it under her name since she was the last one to use the computer?     

I just got this program 2 nights ago & I set it up for my 3 children.  On the first night, my oldest daughter was doing homework & ran out of time.  The program warned her & I was able to give her more time to work on her homework.  Last night, my oldest daughter signed on to this computer before her time curfew.  She did go past her time curfew & signed in 3 or 4 times & was then blocked.  She used the upstairs computer, too.  This morning there were probably a hundred messages saying that she kept trying to sign in every couple of minutes from around 11 pm-3:30 am.  I know that she wasn't up at 3 am.  So tonight when she tried to use the computer, it logged her off because she was out of time for the day.  If the computer was updating Windows or the antivirus program, would it do it under her name since she was the last one to use the computer?