This is happening for me as well. My job was using a specific downstream project, and it would end as expected, not waiting for the downstream job to finish.
But then I edited the job to use a dynamic project name in a variable. Now the job keeps running until the downstream job is finished.
The Trigger Parameterized Build step is the last Post-build step in my job. The job in question and the downstream job are both running on AWS linux instances, and they are different instances. The downstream job launches a new instance when it starts. Not sure if that matters or not.
Jenkins v2.205 and Parameterized Trigger plugin 2.35.2