Warming is expected to intensify hydrological processes and reshape precipitation regimes, which is closely related to water availability for terrestrial ecosystems. Effects of the inter-annual precipitation changes on plant growth are widely concerned. However, it is not well-known how plant growth responds to intra-annual precipitation regime changes. Here, we compiled reanalysis climate data (ERA5) and four satellite-based vegetation indices, including the Normalized Difference Vegetation Index (NDVI), the Enhanced Vegetation Index (EVI), the Solar-induced Chlorophyll Fluorescence (SIF), and the Modified Triangular Vegetation Index (MTVI2), to evaluate the response of alpine grasslands (including alpine meadow and alpine steppe) to the change of precipitation regimes, especially to the intra-annual precipitation regimes on the Tibetan Plateau. We found monthly precipitation over the alpine steppe significantly increased in the growing season (May–September), but precipitation over the alpine meadow significantly increased only in the early growing season (May–June) (MJP) during the past four decades (1979–2019). The inter-annual plant growth (vegetation indices changes) on the alpine meadow was dominated by temperature, but it was driven by precipitation for the alpine steppe. On the intra-annual scale, the temperature sensitivity of the vegetation indices generally decreased but precipitation sensitivity increased during the growing season for both the alpine meadow and steppe. In response to the increase in MJP, we found the temperature sensitivity of the vegetation indices during the mid-growing season (July–August) (MGNDVI, MGEVI, MGSIF, and MGMTVI2) in the alpine meadow significantly increased (p < 0.01) while its precipitation sensitivity significantly decreased (p < 0.01). We infer that more MJP over the meadow may be the result of enhanced evapotranspiration, which is at the expense of soil moisture and even induces soil “drought” in the early growing season. This may be to elevate community water acquisition capacity through altering root mass allocation and community composition, consequently regulating the divergent climate sensitivities of vegetation growth in the mid-growing season. Our findings highlight that it is inadequate to regard precipitation as an indicator of water availability conditions for plant growth, which may limit our understanding of the response and acclimatization of plants to climate change.