Certain embodiments provide improvements to computer technology, by integrating application indicated minimum retention time for tracks to LRU based track demoting schemes in a cache management system of a storage controller having a two-tier cache comprising a DRAM cache and a SCM cache. As a result, caching operations in a storage controller takes account of hints (i.e., indications) provided by an application to retain certain tracks in cache for at least a minimum amount of time. However, the cache is prevented from becoming full (i.e., tracks cannot be staged to the cache) when too many tracks have a minimum retention time. The cache is also prevented from becoming full when too high a percentage of tracks have a minimum retention time. A LRU list is augmented with the information on whether a track has a minimum retention time indicated by an application, and unless the cache is in danger of being full, such requests for minimum retention time is adhered to by the cache management application of the storage controller. As a result, the needs for minimum retention time for a subset of tracks is balanced with the demoting needs of the cache to prevent the cache from becoming full in a two-tier cache. Additionally, time for which a track is maintained in the DRAM cache and SCM cache may be adjusted during promotion of a track to the DRAM cache or to the SCM cache.