Think of every beat of music as being a section of time, rather than a point in time. Each beat consists of the entire length of time from the moment the beat begins right up until the moment the next beat begins. For example, if each beat lasts 1 second (4/4 time at 60 bpm), then the first beat consists of the entire length of time from 1:1:000 to 1:1:999. Beat two doesn't begin until 1:2:000.
When we speak of a note "belonging" to a particular beat, what we mean to say is that it falls within the range of time we define as that beat. Therefore, if you have a series of 4 sixteenth notes "1 e and a", they all "belong" to beat one, because they all fall within its range of time: 1:1:000, 1:1:250, 1:1:500, and 1:1:750.
The last of the four sixteenth notes may be very close to the next beat, and your ear may even perceive it as being "paired up" with the following note, but it is not actually IN the second beat. It is still within the scope of the first beat.
Hope this helps clear it up for you.
Regards,
Jonathan Atkinson
www.ballroomdancers.com