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What gave you the idea that this is an adiabatic system? It's a cup of freshly brewed coffee on your kitchen counter. Equilibrium will certainly not be achieved within 2 minutes. Even if it were, different schemes would reach it at different time points.

It is fundamentally a question about rate of energy transfer.

The thing to notice about the symmetric system is that both items will experience the same rate of transfer. However there's presumably more coffee in your coffee than there is milk so it's not actually symmetric. If you adjust the parameters for volume and specific heat to make the final mixed product symmetric then it no longer matters when you do the mixing.