When are these effects executed? My guess is that they are executed immidietly after a player won that story and before any pending stories are resolved. So that you can first win The Other Path story and put a token on a story without success tokens and then resolve that second story and occasionally put more success tokens on it. Am I right?

Rulebook and FAQ doesn't specify that, and it's a bit confusing, because on the one hand won effects should trigger the moment won, and on the other all stories resolve in one gray box on timing chart.