Thanks for your posting!
I can reproduce the issue with the steps that the TestContainer will not popup the Tooltip, but if we host the UserControl on the Winform the tooltip is OK.
Since the TestContainer is for test only, did you have any special concern about use the UserControl on the Winform
Also I have also test the scenario below.
LinkLabel on UserControl1
UserControl1 on UserControl2
UserControl2 on Windows form,
And the Tooltip is OK.
I am somewhat confused by the last paragraph of your question, if I misunderstood, please feel free to post here.
If you still have any concern, please feel free to post here.