This paper explores the concept of exponential synchronization in neutral-type neural networks with mixed delays over arbitrary time domains. We employ a state feedback controller and formulate the problem using the time scales approach, allowing us to address hybrid time domains that include both continuous and discrete-time domains as a special case. Our approach relies on a combination of time scale calculus and the Banach fixed-point theorem, and leads to less restrictive assumptions compared to other techniques. Importantly, the synchronization criterion derived through this approach reduces to a simple, easy-to-verify linear scalar inequality. Furthermore, we present various special cases of the system under consideration and engage in a comprehensive discussion to highlight the advantages of our findings compared to existing results. We validate the effectiveness of our results through simulated numerical examples over different time domains, including an application to secure communication.