Generative AI is increasingly embedded within learning tasks, yet interaction frequency reveals little about cognitive engagement in student-AI dialogue. Little is known about how such engagement is situated within task workflows or how dialogue characteristics and subsequent task activity relate to students' behaviour and task outcomes. This study examined cognitive engagement in student-AI dialogue, its position within task workflows, and associations of dialogue and task-process characteristics with post-dialogue activity and task outcomes. Data were collected from 1,681 students across 40 university courses using three AI companions embedded in resource creation, peer moderation, and practice. Cognitive engagement in 829 conversation threads was coded with a dialogue-oriented Interactive-Constructive-Active-Passive (ICAP) framework, and 2,969 task sequences were modelled with first-order Markov models. Regression models linked dialogue and task-process characteristics to behavioural re-engagement, peer-rated artefact quality, and practice performance. Passive and Active engagement predominated, although resource creation involved more Constructive and Interactive dialogue, peer moderation more Passive, and practice more Active, while higher-engagement dialogue was less often followed by session termination. In resource creation, student-composed messages were associated with more dialogue-to-task returns than template-only requests at the same Passive level, whereas deeper cognitive engagement was associated with higher final artefact quality independent of return frequency; in practice, AI dialogue after an incorrect attempt was associated with fewer further attempts but higher next-attempt correctness among continuers. Post-dialogue activity and task outcomes are distinct aspects of AI use that interaction frequency cannot capture and evaluations should assess separately.

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