Several states of proton-unbound isotopes Ar-30 and Cl-29 were investigated by measuring their in-flight decay products, S-28 + proton + proton and S-28 + proton, respectively. A refined analysis of S-28-proton angular correlations indicates that the ground state of Ar-30 is located at 2.45(-0.10)(+0.05) MeV above the two-proton emission threshold. The investigation of the decay mechanism of the Ar-30 ground state demonstrates that it has the transition dynamics. In the "transitional" region, the correlation patterns of the decay products present a surprisingly strong sensitivity to the two-proton decay energy of the Ar-30 ground state and the one-proton decay energy as well as the one-proton decay width of the Cl-29 ground state. The comparison of the experimental S-28-proton angular correlations with those resulting from Monte Carlo simulations of the detector response illustrates that other observed Ar-30 excited states decay by sequential emission of protons via intermediate resonances in Cl-29. Based on the findings, the decay schemes of the observed states in Ar-30 and Cl-29 were constructed. For calibration purposes and for checking the performance of the experimental setup, decays of the previously known states of a two-proton emitter Mg-19 were remeasured. Evidences for one new excited state in Mg-19 and two unknown states in Na-18 were found.