Apparently, Zhou has a bit of a tiger mom ruling the show. There was a video on YouTube of them arguing around the time he won junior worlds, but has since been taken down.
I think Tiger mom is a bit of an understatement for his mom. There's a reason she drove him to LA all those years instead of practicing locally...
What’s the difference between tiger parents and your run of the mill skating parent?
Exhibit 1: Vincent's Mom (and his old wikipedia page before someone that wasn't his mom edited it). But, basically, from what I've seen, normal skating parents are intense but do not go to quite the extent of a tiger mom. I don't know how many of these apply to the famous tiger moms of skating (including Vincent's). That is, "skating parents" don't:
-Get on the ice or near the boards to yell at their kid's coaches (or otherwise insert themselves into the lesson)
-Switch coaches behind their current coach's back because they're angry at the current coach (and lie to the new coach so they can do so)
-Switch coaches as soon as any minor failure occurs, even if the coaching is otherwise working out
-Change things out like programs/costume/etc. behind a coach's back
-Correct the coach despite having no meaningful skating experience
-Claim a very competent coach doesn't know what they're talking about
-Build antagonism between the skater and coach because the skater doesn't want to switch coaches
-Homeschool the skater from a young age because a) normal school isn't good enough and b) the skater needs to be on the ice 20+ hours a week from a young age more than he/she needs to be socialized/have friends
-Try to coach the skater themselves for a time before realizing they need a coach, upon which time they harass the coach they're paying thinking they know better
Normal skating parents and tiger moms share a few things - forcing their kids to get on the ice when they don't want to, getting angry at coaches when the kid isn't progressing, etc., but tiger moms take it to a new level.
As an aside, I've actually seen Karen Chen's mom around the rink a few times (albeit when Karen was much younger). She seemed like a skating parent as opposed to a tiger mom. She acted just like any of the other rink moms she was friends with acted.