Maven profile does not affect module earlier in project list - maven

Question

Why won't my run configuration using a maven profile work as intended? Why does the profile fail to skip tests while the parameter does work as intended?
I have a maven run configuration which doesn't run as intended (it runs tests in lib-module which I want skipped):
-pl common,lib-module,my-module test -PdontTestLibProfile
When I run the same run config but using the maven property parameter directly:
-pl common,lib-module,my-module test -DdontTestLib=true the skipping of lib-module tests succeeds.
The maven profile dontTestLibProfile lives in the pom of my-module.
<artifact-id>my-module</artifact-id>
[...]
<profile>
<id>dontTestLibProfile</id>
<properties>
<dontTestLib>true</dontTestLib>
</properties>
</profile>
dontTestLib is a mavenProperty which is checked in the lib-module, where if it is set to true it will not run integration or unit tests.
<artifactId>lib-module</artifactId>
<properties>
<!-- Skip tests: Default is to NOT skip ==> Default is to run -->
<doneTestLib>false</dontTestLib>
</properties>
[...]
<build>
<plugins>
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-failsafe-plugin</artifactId>
<configuration>
<!-- Skip Lib-Module Integration tests if skip is set -->
<skipTests>${dontTestLib}</skipTests>
</configuration>
</plugin>
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-surefire-plugin</artifactId>
<configuration>
<!-- Skip Lib-Module Unit tests if skip is set -->
<skipTests>${dontTestLib}</skipTests>
</configuration>
</plugin>
</plugins>
</build>
Some corollary questions which might be the cause of this issue:
Do maven profiles run in the same sequence as the project list itself, not allowing my-module to affect the lib-module which comes before it?
Do profiles only affect their own POM/module and I am trying to reach outside of the scope?