The tabset border does not encompass the whole HTML Region.The tab regions are floating divs. It's one of those tedious CSS features that a container's height will not increase when its floating content grows (see "Aslett Clearing"). This is fine except for APEX 4.0-themes No. 1, 2, 6, 9 and 11, since there is no clearing attached to some of the region templates.
This will make the outer div embrace all its sub-divs.