Khalai Protoss are susceptible to Amon's puppetry because their nerve cords connect them to the Khala. So when they sever their nerve cords they are cut off from the Khala.
Nerazim Protoss are immune to Amon's puppetry because they already cut off their nerve cords long ago, so they've already been disconnected from the Khala.
The Tal'darim Protoss still have their nerve cords, and still are connected to that Khala, but are immune to Amon's puppetry because...they're already such assholes that Amon flooding the Khala with hatred and anger changes nothing for them?
That about right?