Player has second thoughts regarding aura target
While I agree with John Brian that this sort of thing benefits from actually being there, I also think Jochem has provided enough detail from actually having been there, for me to agree with his resolution.
My philosophy on this: Judges don't do “take-backs”, only opponents can allow those. Judges can rewind when a rule has been broken - i.e., Game Play Error - but the only error here is strategic, and AP had a chance to avoid that by asking for that info before choosing a target for the aura.
Now, in situations where AP says something like “I'll play an Islan… No! Wait! a Swamp”, then - as noted above, and actually being there to get a sense for the length of any pause - I'll probably decide that AP didn't have a chance to gain any info that might influence their change.
In situations where NAP objects to even the smallest changes like this, I might allow AP to complete their action as intended; I might judge that AP did have a chance to see a reaction from NAP, and disallow the change. That's the “had to be there” part.
In this case, AP not only had time to fish for a reaction, they even solicited one with their “how big…?” question. Since many “take-backs” aren't even brought to the attention of a judge, when NAP does object it's often because that particular take-back shouldn't be allowed.
d:^D