I looked closer at the screenshot of HTML you posted above, and I see those div's have closure_uid_###### attributes, which seems to imply the use of Google's closure javascript compiler somewhere in the process. Are you using that on the js code? I assume that the Google uses the closure compiler on the API code, but this is the first time I've seen any manifestation of closure outside the API source.
In any event, I doubt that those divs are responsible for the height change problem, as they are likely present throughout the whole process. Inside the container div for the chart, the API is creating a div that holds the tooltip information. Ideally, this div will be positioned properly over the chart, but it is possible that there is a CSS issue somewhere that is messing with the display of the div.