Are frequency changes of a DDS phase coherent?
No, the frequency changes of a DDS are phase continuous, but not phase coherent. When a new frequency is programmed into the DDS, the next phase will simply be incremental with respect to the last phase value in the phase accumulator, and therefore the output sinewave will be phase continuous. That is, there will be no phase discontinuity, or glitch. You cannot switch from F1 to F2, then back to F1 and expect to be in the same phase as F1 was in originally.