Both accumulated and squashed strategy sets both committer and author to the git user on the Jenkins slave.
The author on the commits on the ready-branch should be kept, as the author on the new commit on the integration branch.
This follows the usual idea of pull-request patterns, where the maintainer accepts the pull requests and becomes the committer, while the original author doing the work get credit as author.
Many repository browsers shows author of commits, thus the history in such systems will be more interesting when looking over the git history. Today it is the git user on the Jenkins slave showing as both committer and author.
If there is more than one commit on the ready branch, the author of the last commit will be used, so in the implementation details we just always use the author of the last commit.