abgeordnetenwatch.de is not your generic community platform - it's a tool that actively creates and enforces communication channels between the people and their political representatives thereby strengthening the democratic process while also being a comprehensive source of information of the political system in Germany.
The answer is... generally run updates first. Whether to import or export the configuration afterwards depends on who updated the contrib code base.
You are updating the contrib code base
If you are updating the contrib code base, run the database updates and then export the configuration, as updates tend to alter the configuration storage data which needs to be commited into the version control system:
When migrating content with the Drupal 8 migrate module, the creation and updating of new entities may fire lots of custom module hooks. This may or may not be desired; if you have found yourself here, it probably interferes with the source data in a problematic way, or unnecessarily slows down the migration process.
The cleanest way I found to stop specific hooks for specific migrations, is to add a dummy/meta field to the migration and check for its value in the hook.