In all cases, readied actions, some immediate actions and attacks of opportunity, game flow is interrupted; an action is started, and that action itself, provokes a response. The response is then resolved, then provided circumstances have not changed, the action that was interrupted continues.
Although an interrupting action is resolved before the action that triggered or provoked it, the response does not retroactively prevent the action from starting.
attack of opportunity
An attack of opportunity "interrupts" the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character’s turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character’s turn).
Then, any time before your next action, you may take the readied action in response to that condition. The action occurs just before the action that triggers it.
Some special abilities or spells use immediate actions in response to other actions (or consequences of other actions, like damage)
an immediate action can be performed at any time — even if it's not your turn.
In most cases, actions may not be split up, so an interrupted action that cannot be continued is no longer available (lost, consumed, wasted, whatever you want to call it). With Tumbling, it is during a move action that the check may be failed, so provided circumstances no longer prevent it, the move action may continue.
Even though an interrupting action is resolved before the action that elicited it, that eliciting action had to start in order to elicit the response.
Tumbling is not unlike moving out of a threatened square; it is the movement that provokes and it is resolved before leaving the threatened square, even though that action is what caused the provocation.
The language is a bit terse in the Tumbling description.
Faliure means you stop... and provoke
It would be preferred had it said something a bit more clear like in Overrun,
If you fail [...] you have to move 5 feet back the way you came, ending your movement there.
Or like in Bull Rush
If you fail [..], you move 5 feet straight back [..]
Overrun makes both the action economy and the movement usage more clear: It takes 5' to step into the opponent's space and 5' to step back out. This is also the language used in Bull Rush.
I think it would be unfair to impose penalties not listed (like interpreting stop as ending your movement), but I do think using the movement cost in Overrun as a guide for tumble makes sense, as both are attempting to move through an enemy's square (as noted in the descriptions under Movement Position and Distance -> Moving through a Square).
The movement cost for tumbling by an enemy is instead like moving out of a threatened square - the movement provokes, but then continues.
So, to answer your specific example, if we use Overrun (and Bull Rush) as our guide; Abe uses 2 squares (10') of movement to approach Bob, two more squares (10') to attempt to move into Bob's square (since it's difficult terrain), where he fails his Tumble and uses two more squares (10') moving back out. If he can otherwise continue (Bob's attack of opportunity didn't change circumstances), Abe would be able to move, although at this point, he's used 30' of a 30' move action.