Cloud-based outsourced Location-based services have profound impacts on various aspects of people's lives but bring security concerns. Existing spatio-temporal data secure retrieval schemes have significant shortcomings regarding dynamic updates, either compromising privacy through leakage during updates (forward insecurity) or incurring excessively high update costs that hinder practical application. Under these circumstances, we first propose a basic filter-based spatio-temporal range query scheme \TrinityI that supports low-cost dynamic updates and automatic expansion. Furthermore, to improve security, reduce storage cost, and false positives, we propose a forward secure and verifiable scheme \TrinityII that simultaneously minimizes storage overhead. A formal security analysis proves that \TrinityI and \TrinityII are Indistinguishable under Selective Chosen-Plaintext Attack (IND-SCPA). Finally, extensive experiments demonstrate that our design \TrinityII significantly reduces storage requirements by 80\%, enables data retrieval at the 1 million-record level in just 0.01 seconds, and achieves 10 $\times$ update efficiency than state-of-art.