In the Job slots and assignments into them tool, you can see actual coverage slots and assignments made into those slots.
Coverage slots - existing assignment
Editing an assignment within a coverage slot is more flexible than in regular slots: you can change the Start date, Start time, and Duration. Note that while creating a new assignment limits you to the start intervals of the slot, you can select any start time here; this is intentional.
Coverage slots - creating an assignment
Creating an assignment starts out the same as with regular slots: right-click on the slot and pick one of the Assign a volunteer... links, or use the Show add person link in the upper left corner. Then it gets complicated.
Depending on how many volunteers are already assigned and when, there can be more than one Opening option. In the example below, we need two volunteers starting on the 8th from 12:45am, and one starting on the 7th at midnight. This is caused by fragmentation of the slot: as assignments are made, if they don't directly abut existing assignments, you end up with smaller gaps where volunteers are still needed.
For any given Opening, the Date is a start date/time during that opening. After selecting a Date, the options for Duration will vary from the smallest assignment time allowed by the slot up to either the longest time allowed or one that would stay within the Opening's time period.