The window has to be open when Alice's photon arrives. Even if it doesn't change the polarisation of the photons, turbulence does affect how fast they travel. To compensate for jitter, a pulse of light is sent 100 nanoseconds ahead of each photon. This timing pulse is affected by the atmosphere in exactly the same way as the photon that follows. So whenever a pulse arrives, the satellite knows that the photon will be coming 100 nanoseconds later and times the opening of the window accordingly.
Turbulence causes another headache too.
Changes in refractive index cause the beam to wander so that it misses the satellite's antenna. To keep the photon beam on course, Alice monitors the feeble reflections from the timing pulses, and uses the information to steer the photon beam. Earlier this year, Hughes set a new record for quantum cryptography through air when he exchanged a key across 500 metres. Each incoming photon encountered a beam splitter, which randomly reflected or transmitted the photon, steering it towards one type of filter or the other. Afterwards, Alice and Bob used an insecure Ethernet link to check for errors in their key.