If the assignment is due at 3 PM, it is late at 3:00:01 PM. Many of my assignments have late penalties automatically computed by my gradebook, and time stamps of emails are imported without adjustments. So, just at the level of the math, it is a "bright line".
On top of this, however, is that I do not extend grace periods. (You can read why below, if interested.)
I consider the last ten minutes before the deadline to be a "high risk" zone:
I always consider such a submission as "rushed" and since many of my assignments are designed around the concept of careful, measured, thought a last minute submissions starts with something of a deficit until the assignment itself proves to me that it was done with care, not rushed.
Sometimes a student submits in a hurry, then resubmits a few minutes later, realizing something was wrong the first time around. I do not guarantee I will use the updated version, and I really don't like double submissions. It gums up the log in process. THINK, then hit the submit button, please!
Servers do NOT always make instantaneous delivery. Your submission time is the time at MY END of the process.
I often have 2 AM or 4 AM deadlines, or such. Please be careful to note whether it is a daytime or nighttime submission.
If the subject line is not correct, I do not feel obligated to consider it as submitted.
Smaller classes with mostly majors are pretty good about deadlines and so, in those classes, sometimes I am less strict about submission time. This "alternate" approach is basically: "Did the submission, in its lateness, waste time at my end or note?" When it didn't (I haven't logged in yet, or the log in was easy, I haven't graded yet, etc.) I sometimes don't track the official late penalties.
I do understand that things happen. If there is an issue, please try writing me about it. Just understand that the excuse needs to be excellent.
Above all, just in terms of fairness, everyone should work under the same rules. There can be exceptions to this, though (accidents and so forth). It is a good idea to communicate with me.
In terms of equally fair treatment of all students, if the deadline is 3PM and I get submissions at, say, 3:01PM, 3:05PM, 3:11PM and so on, when should I decide something is late? If find the only fair-to-everyone place is at 3PM; anything else gets too personal ("Well, for that student maybe I should forgive ..." "For this student who doesn't like me maybe I'll be hard nosed ...")
I ask of students quite a few assignments and nearly all assignments are graded by me and only me. This means I need to coordinate the activity of one, two or three classes, setting up work windows to take care of any particular assignment. When something arrives outside the work window, I have to go back, review the assignment, review the grading rubric, review what I did for other students and then grade the late assignment. Grading the assignment might take 15 minutes, but getting back into the whole framework of the assignment might take 30 minutes on top of that. Hugely, hugely time inefficient and the student runs the risk of me unconsciously giving a harsher grade because of the unpleasantness of it all.
Late submissions usually have an explanation attached, sometimes have follow-up emails by worried students, those emails might require answers by me, I might be required to do special searching to find the missing assignment, I almost always have to revisit my login for that assignment and adjust it, the score might require special adjustments in the grade book at the time of the assignment or at the end of the term, and so forth. All of that uses up my time, even though the lateness was by the student.