We fabricated alpha-phase proton-exchanged (PE) lithium niobate (LN) channel waveguides quasi phase-matched (QPM) via surface periodic poling (SPP) and carried out the first experimental demonstration of second harmonic generation (SHG) in such devices. In order to quantitatively interpret the experimental data, we took into account not only the periodically-poled transverse region providing 1st-order QPM, but also the homogeneously-inverted portion of the waveguides extending below the shallow domains. By a numerical fit of the data we found that, because of the shallow non-inverted domains with depth of the order of 430nm (to be compared with a waveguide depth of 2.6mm), a cascaded process in phase-mismatch gives rise to an effective self-defocusing response which combines with the cubic nonlinearity of the material to provide the measured SHG resonance shift with power.