GEMINI includes hardcoded database versions in its build procedure. GEMINI on Galaxy seems to conform to this; it's slightly confusing because the database build date in the appropriate dropdown for GEMINI load is stated as later than the GEMINI release (0.8.1). However, the underlying data looks to belong to that GEMINI release, so I assume this is just a reflection of when this GEMINI build was incorporated into Galaxy.
I confirmed and the date associated with Gemini indexes is the date that the data was retrieved.
This retrieval uses the same methods as the line-command methods, except they are wrapped in a Galaxy data manager that does some extra formatting/manipulations to the metadata and internal database links. The name given is custom. Whatever version was the current version of the data at that time is what was indexed and included in Galaxy. I don't see a way to view the timestamps on the original files from the source but I don't think that is/was intended to be revealed by the tool authors.
Hope that helps! Jen, Galaxy team