When only one JDK is configured in Jenkins, the drop down for selecting a JDK does not appear. This kind of makes sense because there is no choice to be made, thought it may be helpful see which JDK you are using.

The problem happens when there is a different JRE/JDK used to launch Jenkins than single one configured for Jenkins. A job will pick up the JAVA_HOME from the JRE that launched Jenkins, not the one that is actually configured in Jenkins. If you have 2 JDKs configured in Jenkins and one of them is selected, the job gets the JAVA_HOME from the selected JDK as expected.