It was not an easy thing for Spock to do but when he realized that his Time was upon him, he did not call Jim. While all of him cried out for the alive Jim but Spock knew that this Jim was not his Jim. This Jim was this timelines Spock's T'hy'la and Spock would respect that and would embrace plak tow and finally be reunited with his Jim. It was the only option since the cure to Pon Farr had not yet been discovered and since the scientist who had discovered it in Spock's timeline had died when Nero had destroyed Vulcan it never would be. Spock had no mate and his Time was upon him and since he would never betray Jim by searching for another mate. Of course Spock did not tell anyone that his Time was upon him.
It had been made into law that all must find mates and have to children to continue the Vulcan restoration when their Time was upon them. Something that Spock simply could not and would not do. Jim was the only one he would ever truly be with and certainly the only one that he would ever mate. So Spock would embrace the 'lingering death' and thus embrace death and his reunion. At long last Spock would once again be with his T'hy'la. The fact that Spock rarely spent much time with the Vulcans when not working meant that no one would know what had happened until he failed to show up to the next Council meeting in a week. Which would be by far to late for anyone to do anything.
Once Spock had begun to burn and there was no one there, he would be free.