The "export" part I guess you mean you have that under the Java compiler-project settings ?
Those just relates to classpath exports, not to deployment.
I recall WTP supporting marking a classpath container as something that should be deployed but I can't recall it right now.
btw. you shouldnt be adding any jars to default lib folder - that is very rarely the right solution.
I would recommend you add the jars to the project instead of using a user library for now.