This paper explores an integrated sensing and communication (ISAC) network empowered by multiple active simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs). A base station (BS) furnishes downlink communication to multiple users while concurrently interrogating a sensing target. We jointly optimize the BS transmit beamformer and the reflection/transmission coefficients of every active STAR-RIS in order to maximize the aggregate communication sum-rate, subject to (i) a stringent sensing signal-to-interference-plus-noise ratio (SINR) requirement, (ii) an upper bound on the leakage of confidential information, and (iii) individual hardware and total power constraints at both the BS and the STAR-RISs. The resulting highly non-convex program is tackled with an efficient alternating optimization (AO) framework. First, the original formulation is reformulated into an equivalent yet more tractable representation and partitioned into subproblems. The BS beamformer is updated in closed form via the Karush-Kuhn-Tucker (KKT) conditions, whereas the STAR-RIS reflection and transmission vectors are refined through successive convex approximation (SCA), yielding a semidefinite program that is then solved via semidefinite relaxation. Comprehensive simulations demonstrate that the proposed algorithm delivers substantial sum-rate gains over passive-RIS and single STAR-RIS baselines, all the while rigorously meeting the prescribed sensing and security constraints.