Sort of, but not necessarILy people. Maybe the car arrived late, or got lost; 'happens with ... + <someone doing something>' refers to a recurrent or predictable situation. 'He made the cement too dry, and his wall only lasted a week' 'That always happens with trainee brick-layers.'
Incidentally, some people avoid using 'regularly' in the sense 'commonly/frequently/often', because they look for a regula (Latin, ="rule") when they see that word. I don't expect everyone to apply this principle - which in some circles used to be a prescription - but it may be of interest.