A write operation writes first data to a target logical address range included in a first logical address range of a virtually provisioned device. It is determined that physical storage is not allocated for the target logical address range. First processing is performed to allocate a first portion of physical storage having a first corresponding logical address subrange that includes the target logical address range. The first portion is allocated from a physical device included in a first storage tier. The first processing includes selecting the first storage tier from multiple storage tiers in accordance with selection criteria including metrics characterizing an expected workload or level of activity for the first corresponding logical address subrange of the virtually provisioned device. Mapping information is updated to indicate that the first corresponding logical address subrange of the virtually provisioned device maps to the first portion of physical storage.