Short answer: No
Just change JAVA_HOME to /opt/zing/zing-jdk8 or PATH to /opt/zing/zing-jdk8/bin or your application specific setting to point to the Azul Zulu Prime executable at /opt/zing/zing-jdk8/bin/java.
In general Azul Zulu Prime JVM implements the entire Java Standard Edition standard. That means all fundamental command line parameters are supported per the relevant Java major level specification.
If an -XX command line parameter has no meaning in Azul Zulu Prime JVM (like for instance GC settings for G1 or CMS, which don't exist in Azul Zulu Prime JVM) then those variables are silently ignored. Many -XX parameters are implemented by Azul Zulu Prime JVM, for example -XX:+UseGCLogFileRotation.
With Azul Zulu Prime JVM it isn't expected that you need to tune or optimize any GC settings. The only parameter you might consider to change when switching to Azul Zulu Prime JVM is -Xmx as with Azul Zulu Prime JVM you are not limited to small heap sizes any more.