For more information, please see the article How are Due dates and Penalties Enforced? The article also describes how to see when a student has submitted their work.
To check late submissions before marking is done: click on Students from the main page of the assessment. On the top, right-click "Filter by" and choose "submitted (late)". You can then remove late penalties.
Tip: After the assessment is done, you can change the assessment settings to extend the time limit by some time, for example, 5 minutes. This will mean you don't have to remove the late penalties manually for any student whose submission was less than 5 minutes late.