"Then", meaning next or afterwards, is among a group of adverbs* that link independent clauses. Style manuals, e.g. the AMA Manual or the Mayfield Handbook, tell us that they should be preceded by a semicolon (or full stop). This makes sense since their function (linking sentences) lies beyond the sentence. However, it may be just as common, if not more common, to find "then" preceded by a comma. Also, "then" can link other elements, namely phrases and words. Excluding patterns with "and" before "then", this is what one can find in the dictionaries (albeit at varying frequencies).
(1) She did X, then she did Y.
(2) She did X, then did Y.
(3) She did X, then Y.
This brings up some questions.
Regarding (1), how is this not a comma splice? Is the second clause a supplement? It is even possible to find examples (the examples I found where in user guides or online help) where the comma is absent. So is "then" functioning as a conjunction or is there an elliptical "and" before "then"?
Regarding (2) and (3), are the structures "did X, then did Y" and "X, then Y" compound structures? That is, again, is "then" functioning as a conjunction or is there an elliptical "and" before "then"? If not, what are the structures beginning with "then"?
*This group is called, among other names, conjuncts by Quirk et al, linking adverbials by Biber et al and connective adjuncts by Huddleston and Pullum.