Well, the correct answer up to this point is that we don't know. We would need a theory of quantum gravity to understand what's happening at this scale, and who knows how many ither step further we need to move to have a grasp of the "real" answer. Up to now, we only know that "something" is going to happen, and can make (motivated) conjectures.
It may indeed be that time is discretized in the end, and talking about fractions of planck time is meaningless: maybe the universe computes the next state based on the present one in discrete steps. In your case, it would be meaningless to say that an atom will decay in 10.5 Planck times, the only thing you could see is that at step 10 the atom hasn't decayed and at step 11 it has (barring the correct remark of nsheperd that in practice the time span is too short for decoherence to be relevant). But, honestly, this is all just speculation.
Thanks for the response, that was helpful. I wonder if the question of the continuity of time bears on the idea of the universe computing its next state: if time is discreet, this will work, but if time is continuous, there is no 'next state' (since no two moments are adjacent in a continuous extension). Would this be important to the question of determinism?
Finally, notice that my example doesn't suggest that anything happens in 10.5 planck times, only that one thing begins 10 planck times from now, and another thing begins 10.5 planck times from now. Both processes might only occupy whole numbers of planck times, but the fraction of a planck time is still important to describing the relation between their starting moments.