With ticket JENKINS-24380, the BUILD_ID was changed from timestamp to the build number in version 1.597:

Stop using the formatted timestamp to compute Run.id, and just use the build number as the directory name, so that

This change affected the content of the environment variable BUILD_ID too, becoming equal to the content of BUILD_NUMBER. I used the BUILD_ID variable in my jobs to detect the time, the current build was started. Now I can not do this anymore. Please consider to introduce another variable that will transport the earlier content of BUILD_ID. E.g. create a new environment variable called "BUILD_TIMESTAMP".
So long, I use the EnvInject plugin together with this Groovy script as a workaround:

return [BUILD_TIMESTAMP:currentBuild.getTime().format("yyyy-MM-dd_HH-mm-ss")]

The change makes it also necessary to fix the content of the "env-vars.html" file (help link below a Windows Batch Command entry). Description of BUILD_ID must be changed and BUILD_TIMESTAMP must be added.

The zentimestamp plugin will become invalid after this change. It must be changed to affect the content of the variable BUILD_TIMESTAMP variable.