Halliday & Matthiessen (2014: 618):
Many temporal conjunctives have an ‘internal’ as well as an ‘external’ interpretation (cf. Halliday & Hasan, 1976: Ch. 5; Martin, 1992: Ch. 4; cf. also Mann & Matthiessen, 1991); that is, the time they refer to is the temporal unfolding of the discourse itself, not the temporal sequence of the processes referred to. In terms of the functional components of semantics, it is interpersonal not experiential time. Parallel to the ‘simple’ categories above we can recognise the simple internal ones. These play an important role in argumentative passages in discourse. …
These shade into temporal metaphors of an expanding kind such as meanwhile, at the same time (meanwhile let us not forget that ... , at the same time it must be admitted that ... )
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To be clear, Martin (1992) misunderstands Halliday & Hasan's internal vs external distinction; evidence here.