Space for intruding magma is created by elastic, viscous, and/or plastic deformation of host rocks. Such deformation impacts the geometries of igneous intrusions, particularly sills and dikes. For example, tapered intrusion tips indicate linear-elastic fracturing during emplacement, whereas fluidization of host rocks has been linked to development of elongate magma fingers with rounded tips. Although host rock fluidization has only been observed at the lateral tips of magma fingers, it is assumed to occur at their leading edges (frontal tips) and thereby control their propagation and geometry. Here, we present macro- and microstructural evidence of fluidized sedimentary host rock at the lateral tips of magma fingers emanating from the Shonkin Sag laccolith (Montana, western United States), and we explore whether fluidization could have occurred at their frontal tips. Specifically, we combine heat diffusion modeling and fracture tip velocity estimates to show that: (1) low intrusion tip velocities (≤10−5 m s−1) allow pore fluids ahead of the intrusion to reach temperatures sufficient to cause fluidization, but (2) when tip velocities are high (~0.01–1 m s−1), which is typical for many sheet intrusions, fluidization ahead of propagating tips is inhibited. Our results suggest that intrusion tip velocity (i.e., strain rate) is a first-order control on how rocks accommodate magma. Spatially and temporally varying velocities of lateral and frontal tips suggest that deformation mechanisms at these sites may be decoupled, meaning magma finger formation may not require host rock fluidization. It is thus critical to consider strain rate and three-dimensional intrusion geometry when inferring dominant magma emplacement mechanisms.