For the ToolEnvPlugin, as I comment in the Tool Environment Plugin wiki page, this plugin is not compatible with this plugin.
You have to use the SharedObjects plugin (https://wiki.jenkins-ci.org/display/JENKINS/SharedObjects+Plugin). It covers Tool Env features and has a good integration with the EnvInject plugin.

For the ConfigFileProvider plugin, environment variables are injected by a build wrapper extension. Therefore EnvInject plugin can't capture these new injected environment variables due to Jenkins architecture.
It should be good if the ConfigFileProvider plugin switch to EnvironmentContributionAction

I noticed that the SetEnv plugin is able to get access to the ConfigFileProvider environment variable.
I'm new to Jenkins code, could you kindly point me to an explanation of that shift in behavior?

I think it works due to an order issue (alphabetic order) for the list of wrapper plugin type.
The sentenv plugin might be executed after the ConfigFileProvider.
Could you attach your job configuration file (config.xml)?

Code changed in jenkins
User: Gregory Boissinot
Path:
pom.xml
http://jenkins-ci.org/commit/envinject-plugin/8b24daccd99c5c1e0c72fa5fc19b218f51f69129
Log:
Upgrade to Jenkins 1.437 for fixing JENKINS-14897

Code changed in jenkins
User: Gregory Boissinot
Path:
src/main/java/org/jenkinsci/plugins/envinject/service/EnvInjectVariableGetter.java
http://jenkins-ci.org/commit/envinject-plugin/1adb4759d1a338747d063e3266739d52195d8f67
Log:
Fix JENKINS-14897

Compare: https://github.com/jenkinsci/envinject-plugin/compare/9d7fc88f4e89...1adb4759d1a3

The version 1.68 should fix the issue.

Thank you for the fix. The variable in ConfigFileProvider is injected now.