We do not cease to be responsible for our actions just because we are in a submissive relationship. However, we must be careful not to confuse God's overruling with our own desires and preferences. Unless God has commanded otherwise, we are to obey even silly orders. Submission includes respect. Submission includes prayer.
Submission includes whole-hearted service.
In other words, in submitting, we are not to leave our minds or our hearts or our talents or any other essential element at the door. Part of our submission is to use our minds and hearts in our work and to seek creative ways to assist those who lead us. Submission involves honest communication. The Old Testament prophets sharply criticized many of Israel's kings, but this in itself was a recognition that those kings were the leaders of God's people. Part of submission is a recognition of the authority's right to know what we know.