In this paper, the problem of asynchronous secure controller design for singular perturbation stochastic semi-Markov jump systems (SPSS-MJSs) against complicated cyber-attacks is addressed. Firstly, the unified framework for multi-channel spoofing attacks and DoS attacks is properly established for CPSs with the unreliable communication network. Then, by introducing a register, we propose the memory-based dynamic event-triggered scheme (MDETS), which can save resources for the bandwidth limited network to a certain degree. Since the mode information of Markov chain for the secure controller is often unavailable, a hidden Markov model (HMM) is used to formulate the asynchronous situation between the mode of original system and the constructed controller. Further, by constructing Lyapunov functionals and utilizing linear matrix inequality (LMI) techniques, the obtained closed-loop SPSS-MJSs are endowed with an exponential stability criterion. And the co-design of the asynchronous secure controller and MDETS is presented. Finally, a practical example of the specific small capacitance circuit system is offered to verify the feasibility and superiority of the developed method.