Make sure that the world name isn't disabled in the config.yml.
In order for UltimateTimber to work correctly with custom trees or world generators, you'll have to edit the tree settings. Open the config.yml and find the "trees" section. You can add custom trees here that either match your custom world generator's trees, or any custom trees that you want to make. If the entire tree isn't cutting down correctly, setting the max long distance from trunk to a much higher number should fix the issue.
Additionally, if you want to modify the default settings for trees, you can feel free to do so in the same section.