Temporal knowledge bases associate relational (s,r,o) triples with a set of times (or a single time instant) when the relation is valid. While time-agnostic KB completion (KBC) has witnessed significant research, temporal KB completion (TKBC) is in its early days. In this paper, we consider predicting missing entities (link prediction) and missing time intervals (time prediction) as joint TKBC tasks where entities, relations, and time are all embedded in a uniform, compatible space. We present TIMEPLEX, a novel time-aware KBC method, that also automatically exploits the recurrent nature of some relations and temporal interactions between pairs of relations. TIMEPLEX achieves state-of-the-art performance on both prediction tasks. We also find that existing TKBC models heavily overestimate link prediction performance due to imperfect evaluation mechanisms. In response, we propose improved TKBC evaluation protocols for both link and time prediction tasks, dealing with subtle issues that arise from the partial overlap of time intervals in gold instances and system predictions.