The sensor-augmented RFID system supports applications that are sensitive to environments. To quickly collect the information from all tags, many researchers dedicate on well arranging tag replying orders to avoid signal collisions. Compared to from all tags, collecting information from a part of tags (i.e. target tags) is more challenging because the collecting process is interfered by useless replying from non-target tags. Existing works of target tag information collection are designed for single reader systems. They cannot work efficiently in multi-reader scenarios where each reader lacks knowledge of tag distribution among all the readers. In this paper, we propose time-efficient protocols to collect target tag information in multi-reader systems. The high efficiency of our protocol is enabled by two novel designs. First, we develop a technique that quickly detects and silences non-target tags without a priori knowledge of which tags are in the readers' interrogation regions. Second, we design an allocation vector to efficiently arrange the replying order of only target tags. We further propose an enhancement protocol which can reconcile the collision slots with higher probability and therefore collect information from more target tags simultaneously. Extensive simulation results demonstrate that our protocols significantly outperform the state-of-the-art protocols in terms of time-efficiency.