Parameter-efficient image-to-video transfer adapts frozen image foundation models to video via lightweight trainable adapters. Existing methods insert the same adapter at every transformer layer, implicitly assuming all layers require equal temporal modeling. A layer-wise sensitivity analysis across four video-native model families and two pretraining paradigms reveals that this assumption is wrong: temporal sensitivity increases with depth, and the pretraining paradigm determines its growth profile. Vision-only models exhibit a gradual rise, while vision-language models show early suppression followed by late recovery. This finding motivates STRAP, a training-free adapter placement rule that derives a spatial-to-temporal transition boundary from a paradigm-matched video model. Spatial adapters are assigned before this boundary and temporal adapters after it, without modifying the adapter architecture itself. On four fine-grained action recognition benchmarks, STRAP improves accuracy by up to 11.8% over uniform placement, reduces trainable parameters by 29 to 48%, and lowers inference time by up to 10%. On standard benchmarks, it matches accuracy with fewer parameters. Code is available at https://github.com/th-nesh/STRAP.

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