bai fen zhi bai dui le! What you say looks quite correct. "should" matches pretty exactly with "Yinggai", even to the figurative meanings. We have a saying about "should have":
Should have, could have, would have, but didn't.
As to the present/future sense, it shos that the speaker is considering as real the possibility of not doing the thing.
So, when I hear the word "should", I always think, "there is a 'not' hiding in here". In the past, not is fixed, cannot be changed. In the present and future it is changeable. Compare to I am going to do it, or I am doing it, to I should do it.
Zhu hao,
benjamin