Adrian is saying, well i think he is saying at any rate, that it is reading accurately. The ecu is reading the data, adjusting the fueling and therefore you have a different AFR right afterwards.
Is the tune set up with a target AFR and the ecu compensates based on current AFR? (usual sort of wideband setup).
Also we might want to clarify what you mean by reading accurately. do you mean you expect the figure to be more stable? If so, what sort if range is it going up/down? +-0.05 Lambda?