Responsible, as you will have gathered is used in different senses as an adjective.
One can talk about a responsible person, responsible employee etc. One can also say that the work of an airline captain is a responsible job, meaning it is a job which demands a high level of responsibility. Used in this sense it means the person is reliable, trustworthy and sensible.
In a different sense you can say that a particular person is responsible for the financial affairs of the business. That means it is their job, their duty.
In yet another sense one might ask who was responsible for breaking this window?, meaning Who broke the window?