Ok. I got it now what is wrong with this turning-on-spot problem. It is the animation. Most of the animations are of, let's call it such, 'oriented' type. That is they are somehow flagged for the 'path-finder' that it should align them first with the world axii (or parent bone axii, that I don't know). That is before they start to play the path-finder first makes char turn to what it thinks is the correct orientation of the animation even if it is totaly wrong. This makes a char turn when it appears on this waypoint (came, teleported, or spawned onto it). Then the char plays the animation correctly in-line with its waypoint orientation (turning the waypioint bone does turn the animation on it), this change in orientation results in 'snap-into-animation-stance' glitch. When the animation finishes and next animation takes over the path-finder make our char turn again to align with the world axii if the animation finishes with the char facing somewhere else, this results in 'out-of-the-bed-jump-then-turn-away-then-turn-again-only-then-run' behaviour, same is true if you teleport him, teleport happens right at the end of the animation just before the path-finder do this 'alignment', this is why when a char just appears on a new waypoint path-finder takes this opportunity to 'catch-up' and aligns him on the new waypoint. This rules out teleporting as mean to circumvent it.
All seemed to be lost when three 'non-oriented' animations were discovered and those were: walk, run, crawl. This animations don't care how they are aligned since they are specificaly made to be rotateable mid-playing (making turns while walking). So if you insert an animation just after an oriented one then path-finder doesn't care to align the char anymore so you can then teleport the char without turns. While not helping now (you wouldn't want a char to do a few steps on his bed or better still in the mid-air before running), it gives us hopes for the future when TDW will empower us to change animations, so we will 'disorient' them. All praise all-mighty TDW!
There is as well the cross-compartment bow-wards teleport turning issue, but it seems to be solved, at least for now.
With it given I will now try to do some crew modding, we will have to live with some of this retarded turning for now.