This work introduces an online virtual-physical system-based auto-tuning approach for initializing the parameters of direct adaptive controllers in grid-tied inverters with LCL filters. The method employs frequency-rich excitation signals to ensure sufficient parameter convergence prior to grid connection, effectively eliminating the need for empirical adjustments or offline optimization. A detailed comparison among several excitation strategies is conducted, emphasizing their influence on convergence rate, steady-state accuracy, and robustness of the adaptive process. Unlike data-driven or machine learning (ML)-based controllers, the proposed scheme performs deterministic online adaptation without requiring large datasets, leveraging a virtual system that integrates simulated and real-time measurements. Experimental validation on a 5.5 kW VSI demonstrates a seamless transition to real operation, stable synchronization, and enhanced dynamic and steady-state behavior under grid disturbances and parameter uncertainties, confirming the effectiveness and practicality of the proposed auto-tuning framework for adaptive control applications.