The range of the excitation energy used in the experiment (PIFS) for detecting the fluorescence of water after excitation with synchrotron radiation is from 532 ev to 542 ev. The cross section fluorescence curve show that there is an increase in the fluorescence just above the threshold ionization. This kind of feature appeared also in the case of the CO2 but only after the shake-up photoionization (in the range of 540-590 ev) and the people explain that due to the resonance in shake-up satellites which may increase the number of excited fragments and then enhance fluorescence.
The binding energy of the oxygen 1s electron is around 543 eV. X-rays with energy above this value are more strongly absorbed than those with energy below this value, as the 1s electron can absorb all this energy and be removed from the atom, becoming a photo-electron. This leaves behind a hole in the 1s level. As higher energy electrons fill this hole, they emit light at characteristic energies given by the difference in the electron binding energies.
Perhaps you're asking a more subtle question? The probability of absorbing an X-ray with energies near the binding energy level can be complicated by both chemical environment (NEXAFS/XANES) and by multi-electron excitations (shake-up, and so on).
I would say that PCI (Post Collision Interaction), i.e. recapture of the photoelectron by the molecule once the normal Auger decay takes place (redistribution of electrons in the ionized water molecule). The recaptured electron ends up in an excited/Rydberg orbital of one of the fragments (normal Auger decay most likely will fragment the molecule) which, later on, relaxes by emitting fluorescence.
In some cases, it might also occur that the parent ion does not fragment, producing fluorescence by itself.
Check papers of A. Kivimäki on this issue!
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