It is the doctor in Verdistis that has the tea; search his house, just south west of the park. Specifically, it is <span class='standouttext'>Spoiler : </span><span class='spoiler'>under a hatch, which requires level 5 Lockpick to open</span>. (highlight the text to read)
Save before trying to kill the tree; there is a limited supply of tea and it is fairly easy to set off accidentally. First, you need to click on a tea barrel to open it (you may want to set it on the ground first, rather than leaving it in your inventory). Next, drag and drop it as close to the tree as possible; when an open tea barrel is dropped a poisonous cloud is produced, which will kill the tree. Once dead, you will be able to remove some treasure from it.
