If you run a JBE Build, all activities in the build are done by the user that is used to run the Build Engine. This is typically not jdoe, but a technical user such as build or buildmeister.

The build will usually not replace a baseline, unless you do something like that in the build scripts. A build usually accepts data into a repository workspace, creates a snap shot etc. A build usually does nothing to the stream that is changing it, except creating the snapshot and the baselines related to it. If you want to do anything active (like a deliver), it would have to be done in the build script e.g. using the SCM command line.

There is one exception, which is the post build deliver operation, which today actually does not deliver from the stream you build in the workspace, but replaces the baseline for components in the target green stream with the baseline used in the build. Again, the user that would show in the history should be the user running the build engine, rather than the user requesting the build.