Satellite ocean-color remote sensing is used to detect harmful algal blooms (HABs), yet detection capability does not necessarily ensure reliable interpretation or transferable performance. If these limitations are overlooked when developing cross-regional or global automated HAB early-warning systems, biological claims may be overstated and regional changes in false-alarm or missed-detection rates may go unnoticed, potentially compromising warning reliability and related management decisions. We develop an evidence-constrained framework to evaluate both dimensions: reliability, defined by whether the observation–processing–inference chain supports the intended biological claim, and transferability, defined by whether task-relevant performance is retained under changes in time, region, sensor, or optical environment. A structured Web of Science search yielded 1212 unique records, from which 28 purposively prioritized full-text core studies underwent coding for validation design, cross-domain evidence, error, and uncertainty. The synthesis identifies an evidentiary gap between optical detection capability and biological claim specificity, while fixed-configuration cross-domain evidence was scarce and performance retention remained unquantified. Satellite observations can support bloom presence, optical phenotypes, and selected taxon-targeted applications, but specific claims require specific independent biological references. Reliability is constrained by reference and labeling practices, preprocessing, observation availability, and incomplete uncertainty characterization, while evidence for transferability is limited by insufficient source–target evaluation. We propose a framework linking claim–evidence alignment, independent validation, domain-shift assessment, and uncertainty reporting. Reliable and transferable HAB remote sensing should move beyond detection outputs toward evidence-supported, uncertainty-aware products for monitoring, early warning, and decision-making.