The D-branes in these calculations are static, the string is weakly coupled and the branes are infinitely heavy in the limit. So there are no back-reaction, there are no motion or vibrations of the branes, the whole dynamics of annihilation is just by tachyon condensation, from the point of view of the D0 anti-D0 system, there are just more and more tachyonic strings stuck on. The branes are heavy external sources in this limit.
Obviously, this tachyon condensation cannot go on forever, away from zero coupling, because the D0 branes are not really infinitely heavy. A finite number of strings have to peel off, and leave the D0 branes in an annihilated state, where they are indistinguishable from vacuum, since all the energy has gone off in the outgoing strings. From the point of view of the external theory, the branes annihilated into non-tachyonic strings, and the tachyons on the branes condensed fully, leaving behind an object which doesn't exist anymore--- the annihilated D0 brane system.
The process as calculated in the D-brane picture using perturbative strings doesn't deal with D-brane back-reaction. Ashoke Sen worked to understand the annihilation of branes from tachyon condensation, and concluded that the fully tachyon condensed branes, once the tachyon rolls to its minimum, are no longer there as far as strings are concerned, they can't interact with anything anymore, and so are indistinguishable from vacuum.
Lubos Motl has writted about this interesting story here: http://motls.blogspot.com/2012/08/ashoke-sen-and-tachyon-condensation.html , and links to the most important papers.