Kasha's rule generally holds true for solid-state molecular systems, where the rates of internal conversion and vibrational relaxation are sufficiently higher than the luminescence rate. In contrast, in systems where plasmons and matter interact strongly, the luminescence rate is significantly enhanced, leading to the emergence of luminescence that does not obey Kasha's rule. In this work, we investigate the anti-Kasha emissions of single molecules, free-base and magnesium naphthalocyanine (H2Nc and MgNc), in a plasmonic nanocavity formed between the tip of a scanning tunneling microscope (STM) and metal substrate. A narrow-line tunable laser was employed to precisely reveal the excited-state levels of a single molecule located under the tip and to selectively excite it into a specific excited state, followed by obtaining a STM-photoluminescence (STM-PL) spectrum to reveal the energy relaxation from the state. The excitation to higher-lying states of H2Nc caused various changes in the emission spectrum, such as broadening and the appearance of new peaks, implying the breakdown of Kasha's rule. These observations indicate emissions from the vibrationally excited states in the first singlet excited state (S1) and second singlet excited state (S2), as well as internal conversion from S2 to S1. Moreover, we obtained direct evidence of electronic and vibronic transitions from the vibrationally excited states, from the STM-PL measurements of MgNc. The results obtained herein shed light on the energy dynamics of molecular systems under a plasmonic field and highlight the possibility of obtaining various energy-converting functions using anti-Kasha processes.