For access restrictions, if a student meets the condition then the access restriction is never displayed. The eye is just for setting whether the restriction is displayed greyed-out when a student doesn't meet the condition.
Thus for a date restriction e.g. 'Available until 1 February 2016', this is not displayed to students before 1 February. After 1 February, if the eye is open, the message 'Available until 1 February 2016' is displayed greyed-out.
I assume the reasoning for this is that if a student can access an activity, they don't need to know about the restriction. Regarding assignment deadlines, I would expect them to appear on the student's dashboard
page and maybe also as an upcoming event?