Understanding the constraints that dominant predators impose on subordinate species is important for predicting ecosystem dynamics and anticipating outcomes of predator management. Subordinate predators may avoid dominant predators in time or space, making it difficult to quantify antipredator behaviours unless joint spatiotemporal analyses are used. Here, we test whether an invasive dominant predator (red fox Vulpes vulpes) alters the spatiotemporal activity of an invasive subordinate predator (feral cat Felis catus). We collated records of both species from 3667 camera‐traps deployed experimentally across two regions of south‐eastern Australia with simplified predator guilds. Foxes were poison‐baited in some landscapes within each region. We used generalised additive models to quantify changes in predator spatiotemporal activity across geographic space, vegetation types, human footprints and (artificially manipulated) gradients of dominant predator activity. Foxes and cats had similar diel activity patterns when averaged across all sites, but there was important differentiation at a finer scale: cats did not reduce their spatial activity but shifted diel patterns when localised fox activity was high. Cats were crepuscular on average. However, across dry vegetation types of both regions (where foxes were nocturnal), cats shifted to diurnal behaviour with increasing fox activity. In contrast, fox activity was relatively consistent throughout the daily cycle in the wet forest; here cats avoided dawn when fox activity was high. Changes in cat diel activity patterns may facilitate spatial coexistence between these two invasive predators, potentially shifting feral cat impacts onto different native prey. While it is well‐appreciated that predator activity varies spatially and fluctuates throughout the daily cycle,our study demonstrates that diel activity patterns also vary across space, likely mediated by both landscape‐context and fear. Dominant predator avoidance in time also appears to be spatially dynamic – a key nuance overlooked when simply comparing the average activity overlap between two species.