The Sixth Generation (6G) radio technology is expected to include local 6G networks as a special use case, extending the capabilities of `generic' 6G networks towards more demanding performance requirements. Reconfigurable intelligent surfaces (RISs) offer a novel paradigm for next-generation wireless communications, especially in the context of local 6G networks, enabling advanced signal propagation control through intelligent phase-shift configurations. However, in practical deployments, their performance can be adversely affected by electromagnetic interference (EMI) from external sources and inter-RIS reflections (IRR) caused by signal reflections between multiple colocated RIS units. This paper presents a comprehensive analysis of the joint impact of EMI and IRR in a multi-RIS multi-cell system deployed within an indoor factory environment. A detailed evaluation study is first carried out to investigate their impact on system performance. System-level simulations demonstrate that the joint impact of EMI and IRR degrades system performance more significantly than their individual effects, particularly as RIS dimensions and transmit power increase. To address these adverse effects, an alternate optimization algorithm using the Riemannian conjugate gradient method is then proposed. The novel algorithm optimizes the phase shifts of the RIS elements considering the spatial correlation among their associated channels, and is found to provide up to several orders of magnitude gains in terms of the system sum rate and the outage probability.