In this study, the secrecy performance of reconfigurable intelligent surfaces (RIS)-aided wireless networks in the existence of multiple interferers towards the destination is investigated. In particular, three critical issues in the design of secure RIS-assisted networks are examined: effects of interferers, operation of multiple eavesdroppers (colluding and non-colluding), and benefit of RISs. To examine their effects, the analytical expressions of secrecy outage probability are derived in a closed form. Additionally, asymptotic analyses at a high signal-to-noise ratio (SNR) regime are provided. Finally, the analytical results are validated through numerical simulations.