Synch has to be out DURING the synch (edit: SOS call) process for SOS Chaining, I believe. It's unlike how it works for legends and such where you can just get your lv1 Abra beaten up in Poni Wilds and stick it in first slot, if I remember right.
Edit: for clarity, if you have your Abra out for a SOS chain, that first Pokemon will have a 50% chance of desired nature. But when you throw out your Gyarados or whatever you use for actual chaining, you end up with the game just making a random nature because you aren't using a synchronizer when the process of generating another Pokemon happens. I'm pretty sure you need to stick with the synchronizer during the desired capture period to get the increased specified nature chance.