This note complements and clarifies the results obtained in the original paper {it QCD Parameters Correlations from Heavy Quarkonia} [1] where, here, we present a more detailed discussion of the alpha_s-results obtained @ N2LO at two different subtraction scales mu=2.85 and 9.50 GeV from the (pseudo)scalar heavy quarkonia mass-spliitings M_{chi_{0c(0b)}}-M_{eta_{c(b)}}. We obtain from the M_{chi_{0c}}-M_{eta_{c}} sum rule: alpha_s(2.85)=0.262(9) --> alpha_s(M_tau)=0.318(15) --> alpha_s(M_Z)=0.1183(19)(3) and from the M_{chi_{0b}}-M_{eta_{b}} one: alpha_s(9.50)=0.180(8) --> alpha_s(M_tau)=0.312(27) --> alpha_s(M_Z)=0.1175(32)(3), in complete agreement with the world average: alpha_s(M_Z)=0.1181(11).
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