@martianmister  
The ponies are elements. Celestia and Luna could use them because they were at the time harmonically attuned to the crystals.The Weak point of the elements isn’t the crystals but the ponies themselves which is why at that same point discord targeted the ponies not the gems.

The elements are just focusing crystals that have their own power substructure to amplify the magic power being directed into their crystalline matrix from the element bearer who is literally the element personified. For the most part the crystal are crutch at best. The Elements of Harmony have physical representation within the chosen ones. From birth till adulthood they were and are the physical elements. Each crystals is harmonically tied to each of the elements and can not be welded by someone else for same desired effect. Each Element vibrates a certain way.

Actually, the colors represent the elements and the shapes represent the ponies.

Colors represents elements, not ponies.
 

this is exactly what i thought

What about Pinkie Pie suddenly becoming a member of the Apple family, then?

Oh, I get it now. I kept thinking, “but Fluttershy didn’t get RD’s cutie-mark!” and so-on.

No; the original necklass Elements are still physically theirs.

if their TALENTS changed, then they would have been good at their new jobs. their cutie marks changed but they still had no idea how to do the new jobs because their talent was still their real talent.

@EQUINE_excite  
The talents are unimportant for this story. Those weren’t affected. They switched jobs, and Rarity makes dresses as a job.

@sargesprinkles  
The elements change to match their marks. That’s what happened in the second episode.
 
@TyrannisUmbra  
Given that the destiny switch was explicatively breaking them, I’d say having the cutie marks stay with the pony it was supposed to represent works. Especially since the traits that gave them their real cutie marks stayed in place.
 
The cutie marks on the elements stayed accurate. The cutie marks that were on their rumps are the ones that are wrong.

@lackey_h  
I think you have it backwards; her gem-finding talent is the aid to her fashion, just as RD’s speed talent is an aid to her weather control.

@TyrannisUmbra  
I think the reasoning is that the physical elements represent the ponies themselves, while the colors represent the destinies that have been switched. The outsides stay the same, while the insides change.

Here is a better question - wasn’t Rarity’s cutie mark and talent about finding gems, not the fashion thing which she merely aids with her talent?

@Mr. Horrible  
Yes, but think about it: The butterfly should represent the talent, not the pony, since it’s Fluttershy’s cutie mark, right? Or maybe the shapes still belong to the right pony, because they’re still the right element, but all mixed up? The latter would work for the colors, I suppose.

Looking over the colors, the changed set is what they became, i.e Pinkie Pie’s balloon took on AJ’s orange color of the apple.

They changed to the color of the pony they were changed to, not from. Fluttershy got Pinkie’s talent so her element turned blue, Applejack got Rarity’s so it turned purple, etc.

my question is  
do they change when the new set of ponies gets them  
or do they have to get wielders with similar tattoos?

Congratulations, you figured out the riddle of the sphinx.