Self-supervised speech models (S3Ms) encode a rich hierarchy of acoustic, prosodic, and phonetic information, yet when and where it emerges during pretraining remains unclear. We train frozen-encoder probes on every Transformer layer across pretraining checkpoints of two matched models: HuBERT-Base, whose stage 2 is a separately initialized model trained on new pseudo-label targets, and single-objective wav2vec 2.0-Base. Our five tasks span an acoustic-to-abstract gradient: absolute pitch (F0), speaker-relative pitch, lexical stress, phoneme boundaries, and 38-way phoneme identity. Acoustic-prosodic cues and phone boundaries are decodable from the earliest checkpoints and barely shift across layers, whereas phoneme identity is constructed during pretraining, re-localizing to upper-middle layers under HuBERT's stage-2 targets at a matched update count. Acquisition order therefore tracks abstraction from the acoustic surface, not the segmental/suprasegmental distinction, extending to prosody an account established for phonetic, lexical and syntactic structure; the no-switch wav2vec 2.0 shows no comparable re-localization.
Simultaneous speech translation (SimulST) aims to translate ongoing speech with low latency while preserving translation quality. Recent studies have adopted large language models (LLMs) for SimulST and formulated it as a multi-turn dialogue task for efficient generation, achieving state-of-the-art performance. However, existing dialogue-style SimulST approaches typically rely on specialized training schemes to acquire simultaneous translation behavior, either using synthesized read/write trajectories, which may provide suboptimal training signals, or jointly optimizing translation quality and latency, whose competing objectives may cause optimization instability. In this paper, we introduce SimPOTrans, a reinforcement learning (RL) framework that enables offline speech translation models to self-adapt to dialogue-style SimulST. Through a simple two-stage RL post-training pipeline, SimPOTrans rewards an offline model for exhibiting translation behaviors beneficial to simultaneous scenarios when given partial speech inputs, thereby enabling offline-to-simultaneous self-adaptation without synthesized read/write trajectories or explicit latency optimization. At inference time, SimPOTrans requires no external decision policy and enables flexible quality--latency control by simply adjusting the chunk size of speech input. Experiments on the ACL 60/60 and MCIF benchmarks across three language directions (En$\rightarrow$De, En$\rightarrow$Zh, and En$\rightarrow$Ja) demonstrate that SimPOTrans outperforms several strong baselines, achieving a superior quality--latency trade-off.