I'd say that most hard determinist positions hold that there never was a point where a different outcome was inevitable, you were always going to change your mind.
Your thought experiment doesn't work because it relies on the positing of two different alternative outcomes when hard determinism only allows for one.
It is not an after-the-event phenomenon, but it is not one which is useful to humans either. A belief in hard determinism does not mean that one can in fact predict what is going to happen. If one were posessed of both complete knowledge about every factor affecting an event, including any factors our science does not yet recognise, and of the neccessary computing or mental power to accurately calculate the effects of all those factors then one should be able to predict the future with 100% acuracy.
Such a depth of knowledge is clearly impossible for us especially since we don't know if there are other hidden factors which might be involved.
As well as being practically impossible such knowledge may also be theroretically impossible if there is a truly random fundamental basis to the behaviour of certain elements affecting the event.
TTFN,
WK
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