Undergrad Decoherence and direction of causality

[entropy1]

If I use the expression $(|A\rangle+|B\rangle)|M\rangle \rightarrow |A\rangle|M_A\rangle+|B\rangle|M_B\rangle$ for decoherence, does that mean that we can infer that, IF the measured value is $A$ that THEN we will measure $M_A$, OR that IF we measure $M_A$ THEN the measured value must have had the value $A$? Are both legitimate?

 

[entropy1]

Little bump because I rephrased the question a little.

I think the answer to my question involves entanglement. If so it would be appreciated to have it explained in the context of my question. Thanks!