Knowing Pokemon-devs, it isn't a "glitch". Its an obscure quality-of-life improvement.You only need one Synchronizer of any nature for getting specific-natured mons from SOS battles.
There is a glitch with Synch + SOS battles whereby a Pokemon with Synchronize must be on the field when the new Ally appears, but the nature will be synched with the first Pokemon in your party, regardless of whether the first pokemon in your party is the Synchronize pokemon. So just raise one Synchronizer to a sufficient level with the moves you want (Trick/Sub/CM/Psybeam in your case), and then put any random pokemon with the nature you want at the lead of your party. The lead mon can be fainted, if you don't want it to actually appear in the battle at all -- the Synchronize will still work.
This glitch only exists when Synchronizing allies in SOS battles. Otherwise synching natures is the same as previous gens.
Just like the "trapped circle" in front of the Nursery where you can ride on Tauros perpetually without moving. Somebody definitely put that there on purpose. Its too perfect.