In the fifth-generation and beyond era, reconfigurable intelligent surface (RIS) and dynamic metasurface antennas (DMAs) are emerging metamaterials keeping up with the demand for high-quality wireless communication services, which promote the diversification of portable wireless terminals. However, along with the rapid expansion of wireless devices, the electromagnetic (EM) radiation increases unceasingly and inevitably affects public health, which requires a limited exposure level in the transmission design. To reduce the EM radiation and preserve the quality of communication service, we investigate the spectral efficiency (SE) maximization with EM constraints for uplink transmission in hybrid RIS and DMA assisted multiuser multiple-input multiple-output systems. Specifically, alternating optimization is adopted to optimize the transmit covariance, RIS phase shift, and DMA weight matrices. We first figure out the water-filling solutions of transmit covariance matrices with given RIS and DMA parameters. Then, the RIS phase shift matrix is optimized via the weighted minimum mean square error, block coordinate descent and minorization-maximization methods. Furthermore, we solve the unconstrainted DMA weight matrix optimization problem in closed form and then design the DMA weight matrix to approach this performance under DMA constraints. Numerical results confirm the effectiveness of the EM aware SE maximization transmission scheme over the conventional baselines.