If you define variables in a style repository they will also appear and be available in the projects to which the repository is linked. When you link the repository, all the variables in the repository that do not exist in the project are copied to the project. Variables that already exist in the projects are left unchanged; their values do not update with different values from the repository.
At present, this is really just a convenience for sharing variables to multiple projects. The values of the variables are not dynamically linked, even if the styles are. The values of the variables in your projects will NOT update when their values are changed in the repository. This is the same as existing variables in the project, which are not updated with the values of repository variables when you link a repository.
The only way to force the values of a variable in a project to update with a changed value in the repository is to delete the variable in the project. Then the variable will appear again with the new value from the linked repository the next time the project is loaded. However, this is not really very practical, because you would need to do this for all the variables in all your projects every time you change the values of the variables in the repository.