Fix exception in ApiPageSet

ApiPageSet is calling $this->profileOut(), then calling a function that
calls $this->profileDBIn(). Move that function to after a new
$this->profileIn().

Also, add a unit test for this situation.

Bug: 51821
Change-Id: Ib4dbfb567faadcd5e3d7d058ca6bdf8b4c83f634
Merge "Fix exception in ApiPageSet"