The existence of correlated nucleosynthetic heterogeneities in solar system reservoirs is now well demonstrated for numerous nuclides. However, it has proven difficult to discriminate between the two disparate processes that can explain such correlated variability: incomplete mixing of presolar material or secondary processing of a well-mixed disk. Using stepwise acid-leaching of the Ivuna CI-chondrite, we show that unlike other nuclides such as Cr and Ti, Sr-isotope variability is the result of a carrier depleted in Sr. The carrier is most likely presolar SiC, which is known to have both high Sr-concentrations relative to solar abundances and extremely depleted Sr compositions. Thus, variability in Sr in meteorites and their components can be attributed to varying contributions from presolar SiC. The observed Sr excesses in calcium-aluminum refractory inclusions (CAIs) suggest their formation from an SiC-free gaseous reservoir, whereas the Sr depletions present in differentiated meteorites require their formation from material with an increased concentration of SiC relative to CI chondrites. The presence of a positive correlation between Sr and Cr, despite being hosted in carriers of negative and positive anomalies, respectively, is not compatible with incomplete mixing of presolar material but instead suggests that the solar system's nucleosynthetic heterogeneity reflects selective thermal processing of dust. Based on vaporization experiments of SiC under nebular conditions, the lack of SiC material in the CAI-forming gas inferred from our data requires that the duration of thermal processing of dust resulting in the vaporization of CAI precursors was extremely short-lived, possibly lasting only hours to days.