Working with dates is usually a headache, and for that, we have tried to keep it as simple as possible. That's the way Exporter is managing dates:
Dates will be exported with the timezone of the user who's doing the export process.
We're working with this as Jira is doing, you don't have to configure anything else.
We're using the format you've configured on the Look and Feel section under the System part of the Jira administration.
It doesn't matter the export format, dates will be rendered as the "Complete Date/Time Format" configuration.
But, on Exporter Server, we're not rendering dates on our dashboard that way, due to internal limitations. You will see dates in "dd/MMM/yy" format and datetimes in "dd/MMM/yy h:mm a" format. But, do not be worried, your exports will follow your Jira configurations as it's explained above.