I just ran some thorough tests. The new version is definitely an improvement and much smarter than before.
I don't necessarily expect it to 'move toward' 3rd ring resources in anticipation of aquiring them; rather it follows its rules for 2nd ring and if at that time a resource is adjacent in the 3rd ring in bumps up the priority a bit.
Actually, that's one of the awesome improvements Firaxis has made. For example, the city will actually prioritize 2nd ring tiles that are adjacent to a 3rd ring resource, when normally, they would be equal in influence cost to other 2nd ring tiles. It makes it less of a random shot to grab that adjacent tile so you can grab the resource next.
Another nice thing is that it seems to prioritize luxury resources over bonus resources. Though, sometimes it doesn't and I'm not sure whether it's because they were in the first ring or if it's another smart coding to increase the priority of bonus resources for the first couple acquisitions to get the city off to a good start.
But, with regards to luxury vs. bonus, another smart move which was pretty evident during the tests is that it won't care much for bonus luxuries that are past the 3rd ring and are unworkable, but luxuries it will go after -- which is the way it should be.
Anyway, with some tweaks, I greatly improved the order in which cities acquire tiles. You'll no longer come across those odd instances where a resource is adjacent to your borders, yet it's grabbing normal tiles.
I created two versions, one that is a "Lite" one and will simply fix the problem you ran into for players that don't wish to modify the base game too much or are wary doing so, and another version which further tweaks some more values to make the acquisition order very efficient.
I'm just polishing up the the two versions to a "publishable" state by writing some descriptions and creating some images.