Noticing a contradiction when making a statement is just one way writers find contradictions, and that kind of immediate noticing would only be for obvious contradictions.
There are tons of other things you do, like recalling relevant facts related to the new statement and making sure the statement fits into the facts. You go through a timeline, make sure the statement fits into the timeline. You look at the implications of the statement, make sure those fit with other relevant facts. You opt to do these things depending on what the sentence means and implies. This is not just you "noticing" a contradiction, it's a process.
And what does how real brains work mean anyway. You can't compare writers thinking and writing a novel to some six year old writing a paragraph.
There are tons of other things you do, like recalling relevant facts related to the new statement and making sure the statement fits into the facts. You go through a timeline, make sure the statement fits into the timeline. You look at the implications of the statement, make sure those fit with other relevant facts. You opt to do these things depending on what the sentence means and implies. This is not just you "noticing" a contradiction, it's a process.
And what does how real brains work mean anyway. You can't compare writers thinking and writing a novel to some six year old writing a paragraph.