Reconfigurable intelligent surfaces (RIS) are currently drawing a lot of attention in the research community as a key technology for future wireless networks. In addition to boosting the signal-to-noise ratio and improving coverage for cellular users, they can also be used to transmit locally collected data either by partitioning the RIS array into tiles and mapping the local data to the indexes of the activated tiles (or groups of tiles) following the concept of spatial modulation (SM), or by activating all RIS elements and mapping the local data onto a set of common phase shifts. The problem of the first technique, which we refer to as RIS-SM, is that spatial correlation between elements of the RIS array strongly degrades the bit error rate performance. In this paper, we focus on the second technique, and we investigate the transmission of low bit rate local data using the concept of hierarchical transmission. The basic idea behind this technique is that the magnitude of the common phase shifts must be maintained at a very small value in order to keep the performance degradation caused by the local data on the user data within an acceptable limit. For the local RIS data, this constraint leads to a small minimum Euclidean distance in the signal constellation plane, but despite this small minimum distance, the desired performance is achieved by limiting the speed of the local RIS data to a fraction of the user symbol rate. Analytic minimum distance calculations and simulation results are provided to demonstrate the efficiency of the proposed hierarchical transmission technique.