Currently, there is no event which is fired when the Tooltips are shown.
Still, they should hide automatically, but after testing the scenario I noticed that there is an issue with the Map widget.
I created an issue in our GitHub repository and forwarded it to our developers for investigation. You can track its progress at:
Unfortunately, for now, there is no workaround available, but if there is one it will be added in the issue.
Additionally, I updated your Telerik points for bringing this to our attention.
Telerik by Progress