<p>In this paper, we propose a novel alternated inertial iterative algorithm with a self-adaptive step size for approximating solutions to split variational inequality problems in real Hilbert spaces. A key feature of the proposed method is its strong convergence guarantee under the quasimonotonicity of the involved operators, which is a strictly weaker assumption than pseudomonotonicity and monotonicity. Notably, the algorithm does not require any prior knowledge of the norm of the transfer operator or the Lipschitz constants of the cost operators. Moreover, by relaxing the restrictions on several control parameters, the admissible range of step sizes is significantly enlarged, thereby enhancing the flexibility of the method. Extensive numerical experiments, including both finite- and infinite-dimensional test problems as well as simulations arising from optimal control applications, are conducted to assess the performance of the proposed algorithm. Finally, the applicability of the proposed framework is further illustrated through a stylized traffic network equilibrium problem between two cities, where the associated cost operator is quasimonotone but not pseudomonotone.</p>