@Kaarin:
While that information doesn't contradict what ringkichard posted, I do think it's pertinent to point out that it was written before Move Actions had steps, and is thus somewhat outdated. The steps for a Move Action are the most recent ruling and would take precedence, which actually have been slightly updated as well since the quote from ringkichard. The current steps are:
1. Declare Move
2. Pay Costs
3. Leaving Zone Effects
4. Walls
5. Move
6. Entering Zone Effects
A creature is never in more than one zone, and is subject to whatever effects may be present within that zone. Thus, before step 5 it is subject to whatever effects are in it's starting zone, and after step 5 it is subject to the effects of the new zone it is in. This is different from "Leaving Zone Effects" and "Entering Zone Effects" which are specific spell effects that only trigger upon leaving or entering a zone. General effects such as Gravikor only care about what zone you are currently in, which is only changed during step 5 of a Move Action.
This should also answer GW's question. You change what zone you are in during step 5, and then trigger any Entering Zone Effects that are in that zone during step 6. If contradictory zone effects are present, it would follow the rules of multiple effects outlined on pages 8 & 9 of the Rules Supplement, which is that they are applied in order of their timestamp, with the later effects taking precedent.