Proactive task-oriented agents must autonomously anticipate user needs, identify actionable opportunities, and trigger software actions at appropriate moments - fundamentally shifting from reactive systems that await explicit instructions. However, existing approaches lack generalizable end-to-end solutions for measuring and optimizing such anticipatory behaviors. This paper introduces ProActor, a unified framework for conversational task scheduling that integrates: (1) a domain-agnostic automated annotation methodology that enables scalable proactiveness reinforcement learning (RL) by generating full opportunity time windows instead of rigid point labels, (2) systematic proactiveness metrics capturing both timing quality and reference action alignment, and (3) RL optimization using GRPO with various reward designs. Our insight is that RULER-based rewards with proactiveness rubrics are crucial for improving timing quality, and that proactiveness optimization enabled by stage-aware composite rewards is key to balancing timing quality and reference action alignment. Timing-aware RL requires extensive exploration, demanding efficient infrastructure. We develop ART-F, an adaptive framework combining request-adaptive inference clusters with DDP-based training on single-node multi-GPU systems, enabling LoRA training of 4-bit Qwen2.5-14B-ProActor-Q4 with 4-8x speedups. Experiments on two newly auto-annotated datasets demonstrate significant improvements in proactive timing while maintaining action consistency comparable to state-of-the-art (SOTA) baselines. Ablations validate the effectiveness of distinct composite reward variations.