Awfully familiar actually. I read a quote by Morihei Ueshiba in an interview once, someone (wish I could remember who) was being interviewed and said that the founder would often say things like "A man stands between the Heaven and the Earth", which the person being interviewed viewed as a rather outlandish way of saying 'stand up straight'. He was likely correct in that what the founder probably meant was 'stand up straight', but he had some other things in mind too it seems. When I teach these things I usually try telling people to stand up straight and make themselves as tall as they can, then allow yourself to relax downwards from that posture.
I usually tell people that if a limb is being moved you have to imagine the tester isn't actually trying to move your limb, but they are in fact trying to move your centre, similar to what you described. The advantage that the many different ki tests have is that they put you in a variety of body positions both static and dynamic which make such coordination difficult, usually if you try to concentrate on copying only the movements you will fail the ki test. Often once you start to get the basic idea and can do the simpler ki tests you fail the tests which involve movement. You tend to be strong at the beginning and end of the movement and weak in the middle.
Who said this stuff wasn't in aikido...?
I dunno.... see my post about "nikkyo" to understand my perspective. So far, nothing you have said indicated to me that you already do these things quite to the full level. You may be doing a variant (like in the nikkyo example), but I'd bet good money that in many ways you're doing something quite different. The reason I say that is that this stuff is tricky to learn and someone who really does it would have said something noting the differences rather than indicating that it's normal stuff. If someone really can do the tricky stuff that it takes to understand this, they know the tricky stuff is there... if you see what I mean. The general descriptions, like in the nikkyo example, sound the same to someone who can do something close to it, but there's a very clear difference. And again, for the umpteenth time, I'm really careful about this stuff because I've been at times the student on the receiving end of some wasted years by teachers who thought they already "knew this stuff". It's not a "who's superior" sort of peeing match at all.
Incidentally, there have been people who posted on this forum (and others) that I can tell they do indeed understand the basics of this stuff (Dan or Rob would be examples that pop to mind, but there are a few others). But there are levels of this stuff. I can tell where someone's level generally tops off by the way they describe things; and I'll bet someone better than me can understand where my level tops off. But I would be able to spot who was better than me from what they say... then I'd go check them out personally and I'd learn from them. The last thing I'd try to do would be to argue them to a standstill because I would, as I've said before, prefer to progress myself than to impress beginners or students. I'm always looking to learn. Maybe that's why I don't spend my time having a school and being a teacher. I don't think I'm good enough yet.