Halliday & Matthiessen (2014: 182n):
We see the difference in orientation between mood Adjuncts such as certainly and modal Finites such as must in the tag. With the subjective type, the speaker gives his or her subjective assessment, and then asks for the addressee’s subjective assessment: they must’ve left, mustn’t they? In contrast, with the objective type, the speaker does not ask for the addressee’s subjective assessment; the modality is not part of the tag: they certainly left, didn’t they? Similarly, can they have left? means ‘in your opinion, have they left?’, but have they perhaps left? means ‘have they left? – it is possible’ (cf. haven’t they left?: ‘have they left? – I thought it was so’). In other words, with the subjective orientation, the modality is queried, but not with the objective orientation.