Criteria for interpreting story phases certainly need elaborating. We can say that neither grammar nor discourse semantics are reliable criteria. Phases are units at the level of register, so we need criteria from field and tenor, that may not be explicit in the text. …
 Given that 'story' is an instance type (genre) of language, "criteria for interpreting story phases" will include evidence from the content plane of language: semantics and lexicogrammar. On the other hand, it is true that discourse semantics offers no reliable criteria, but this is because it is theorised on multiple misunderstandings of SFL theory and riddled with internal inconsistencies, as demonstrated in great detail here.
 Here Rose uncritically repeats Martin's (1992) theoretical error of mistaking varying language subpotentials (register) for context potential (field, tenor mode), and then complicates the confusion by attributing proposed phases of a text (semantics) to context misconstrued as register.
That is to say, in terms of the theoretical architecture, there are two dimensions of misunderstanding here: stratification and instantiation. In terms of stratification, Rose confuses semantics with cultural context, while in terms of instantiation, Rose confuses system (potential) with subsystem variation (register).