In the era of information explosion, numerous items emerge every day, especially in feed scenarios. Due to the limited system display slots and user browsing attention, various recommendation systems are designed not only to satisfy users' personalized information needs but also to allocate items' exposure. However, recent recommendation studies mainly focus on modeling user preferences to present satisfying results and maximize user interactions, while paying little attention to developing item-side fair exposure mechanisms for rational information delivery. This may lead to serious resource allocation problems on the item side, such as the Snowball Effect. Furthermore, unfair exposure mechanisms may hurt recommendation performance. In this paper, we call for a shift of attention from modeling user preferences to developing fair exposure mechanisms for items. We first conduct empirical analyses of feed scenarios to explore exposure problems between items with distinct uploaded times. This points out that unfair exposure caused by the time factor may be the major cause of the Snowball Effect. Then, we propose to explicitly model item-level customized timeliness distribution, Global Residual Value (GRV), for fair resource allocation. This GRV module is introduced into recommendations with the designed Timeliness-aware Fair Recommendation Framework (TaFR). Extensive experiments on two datasets demonstrate that TaFR achieves consistent improvements with various backbone recommendation models. By modeling item-side customized Global Residual Value, we achieve a fairer distribution of resources and, at the same time, improve recommendation performance.