The rising demand for energy and spectrum resources in next-generation Internet-of-things (IoT) systems accounts for innovative modes of information and power transfer. One potential solution is to harness the active transmission capability of devices to facilitate data transmission and wireless energy harvesting (WEH) for backscatter communication so as to form a symbiotic radio (SR) environment in a mutualistic manner. Additionally, incorporating reconfigurable intelligent surfaces (RISs) into the SR environment can provide an additional link and enhance the reliability of backscatter communication, thereby reinforcing the symbiotic relationships between active and passive devices. This paper proposes a novel SR system where a standalone RIS sustains its functions through WEH based on a low-power RIS structure and establishes mutualistic symbiosis by utilizing a signal conveyed by the primary transmitter (PTx) to assist ongoing transmissions and convey information to the primary receiver (PRx). The PTx employs time index modulation (TIM) to transmit information to the PRx and power to the RIS and energy harvester (EH). A log-likelihood ratio (LLR)-based detector is presented to address challenges in the TIM scheme. Finally, the performance of the proposed scheme is investigated in terms of harvested direct current (DC) power at the RIS and EH, as well as the bit error rate (BER) at the PRx.