This study reports mechanisms of electron power absorption in radio frequency (RF) plasmas with inverse (negatively charged) sheaths, which are caused by strong thermionic electron emission from the electrode surface. Based on particle-in-cell/Monte-Carlo collision simulations and the moment analysis of the Boltzmann equation, we confirm that this thermionic-emission-driven RF plasma features more intense electron heating in the bulk plasma, which differs from capacitive RF discharges. We reveal that non-local collisional heating can still be the dominant electron power absorption mechanism even when the strong electric field penetrates across the gap in an RF discharge. Furthermore, a transition of the dominant heating mode from non-local collisional to Ohmic is demonstrated as the gas pressure increases in RF plasmas with inverse sheaths.