The factors that determine the characteristic seasonality of influenza remain enigmatic. Current models predict that occurrences of influenza outside the normal surveillance season within a temperate region largely reflect the importation of viruses from the alternate hemisphere or from equatorial regions in Asia. To help reveal the drivers of seasonality we investigated the origins and evolution of influenza viruses sampled during inter-seasonal periods in Australia. To this end we conducted an expansive phylogenetic analysis of 9912, 3804, and 3941 hemagglutinnin (HA) sequences from influenza A/H1N1pdm, A/H3N2, and B, respectively, collected globally during the period 2009-2014. Of the 1475 viruses sampled from Australia, 396 (26.8% of Australian, or 2.2% of global set) were sampled outside the monitored temperate influenza surveillance season (1 May - 31 October). Notably, rather than simply reflecting short-lived importations of virus from global localities with higher influenza prevalence, we documented a variety of more complex inter-seasonal transmission patterns including "stragglers" from the preceding season and "heralds" of the forthcoming season, and which included viruses sampled from clearly temperate regions within Australia. We also provide evidence for the persistence of influenza B virus between epidemic seasons, in which transmission of a viral lineage begins in one season and continues throughout the inter-seasonal period into the following season. Strikingly, a disproportionately high number of inter-seasonal influenza transmission events occurred in tropical and subtropical regions of Australia, providing further evidence that climate plays an important role in shaping patterns of influenza seasonality.