After installing the Timestamper Plugin, you have to configure each job by manually checking the "Add timestamps to the Console Output" option.

Obviously, it can be a bit cumbersome. But here comes the great groovy script console again.

With the following simple script, you can activate the option on every jobs of your server in just one go.

Backup your config before playing with those scripts, as always

for (item in Hudson.instance.items) {
  println("\njob: $item.name")
  hasTimestamper = false;
  item.buildWrappersList.each {
    if (it instanceof hudson.plugins.timestamper.TimestamperBuildWrapper) {
      hasTimestamper = true;
    }
  }
  if (!hasTimestamper) {
    println(">>>>>>>> Adding timestamper right to $item.name")
    item.buildWrappersList.add(new hudson.plugins.timestamper.TimestamperBuildWrapper());
    item.save()
  }
}