Beaming is correlated to meter (metre) and is a publishing device to facilitate music reading for the performer. It doesn't always have to be on a beat if the figure starts with a rest.
For example:
Notice the second and third groups. The beaming starts on a note after the beat. In these cases the rest is on the beat yet the group is still beamed.
I tried to make a group with the first note with a flag and the next three sixteenth notes beamed but the software seems to be preventing it. i.e. the software thinks it is a bad idea
I hope that helps.
Eric