I recently re-configured our TeamCity build configuration to take advantage of the Branch features to apply the same build configuration to multiple branches in the same reposit
From the linked page adding the QueryString param worked for me:
?branch=
Without this it only downloads artifacts from default branch.
Our full url:
http:///repository/downloadAll//.lastFinished?branch=
Which will download latest build from branch 'branchname' on the 'buildid' config.