Integrated sensing and communication (ISAC) is a promising solution to mitigate the increasing congestion of the wireless spectrum. In this paper, we investigate the short packet communication regime within an ISAC system assisted by a reconfigurable intelligent surface (RIS) to meet the low latency ultra-reliable requirements in the next-generation wireless networks. We consider a non-ideal RIS model that captures effects of the phase-dependent amplitude variations in the reflection coefficients, and we have incorporated the near-field model into the channels between the RIS and the users or targets. In this setup, we jointly design the transmit beamforming and the RIS phase shifts to maximize the sum rate while satisfying the sensing signal-to-noise ratio (SNR) requirement. The system simultaneously carries out multitarget sensing and multi-user short packet communications with the help of the RIS. Considering the nonconvex and dynamic nature of the resulting optimization problem, we propose an asynchronous advantage actor-critic (A3C) based method for beamforming and reflection design in this setup. Numerical results demonstrate the superiority of the proposed scheme over the benchmarks.