What decides whether a card is exiled or returned as a player loses?
There is a subtle difference between your two examples:


The Act of Treason'd Runeclaw Bear is under Alex's control because of a control changing continuous effect.
The Serra Angel is put into play under Alex's Control.


This is a subtle but important difference. Whenever a creature enters the battlefield, whoever controls it at the time is considered to be its controller. Usually this means that the person who owns the creature is also the controller but because of cards like Bribery that isn't always true. This is covered in the comprehensive rules:


  110.2.: A permanent’s owner is the same as the owner of the card that represents it (unless it’s a token; see rule 110.5a). A permanent’s controller is, by default, the player under whose control it entered the battlefield. Every permanent has a controller.
  110.2a: If an effect instructs a player to put an object onto the battlefield, that object enters the battlefield under that player’s control unless the effect states otherwise.


This is different from an effect such as Act of Treason that causes a creature to change controllers. These effects are called continuous effects and are treated a bit differently.


  611.1.: A continuous effect modifies characteristics of objects, modifies control of objects, or affects players or the rules of the game, for a fixed or indefinite period.


So to bring this together lets have a look at what happens when a player loses the game:


  800.4a: When a player leaves the game, all objects (see rule 109) owned by that player leave the game and any effects which give that player control of any objects or players end. Then, if that player controlled any objects on the stack not represented by cards, those objects cease to exist. Then, if there are any objects still controlled by that player, those objects are exiled. This is not a state-based action. It happens as soon as the player leaves the game. If the player who left the game had priority at the time he or she left, priority passes to the next player in turn order who’s still in the game.


So in your first example you can see that the Runeclaw Bear is under Alex's control because of a effect which gave him control. When Alex leaves the game this effect ends, so the Bears revert to Binaca's control.

In your second example Serra Angel doesn't have any control changing effects applied to it, so those effects can not end (they never started). Instead it is just treated as any other permanent that is controlled by Alex and is removed from the game.


Additional Notes: One thing I figure I should mention is that not all control changing continuous effects are temporary like Act of Treason. Cards like Beguiler of Wills will give you permanent control of the creature, but will still be treated the same as Act of Treason when the player leaves the game.

Secondly, you are correct in that the game only knows the controller and owner of permanents. That is why in your second example Alex loses the Serra Angel when Bianca leaves the game, she owns the card so it will leave the game with her.