timeclock mofo-ery

So, I don't know if this is legal or not (it doesn't seem like it should be!) but it's definitely shitty.
The timeclock in the library I work at rounds your punches to the nearest quarter-hour. So, if I punch in at 8:55 for my 9am shift, it rounds it to 9am, and I don't get paid for those 5 minutes. Not a lot, I know, but over time it can add up.
If I'm 5 minutes late (and I'm rarely late) it also rounds it to 9am, so my pay isn't docked - but if I were frequently late, even by just a couple minutes, I'd get in trouble.
But if I'm more than 7 minutes late, it rounds it to 15 minutes, so if I'm 8 minutes late I lose 15 minutes of pay.
And if I happen to be early, and clock in at say, 8:45, my manager just manually adjusts it so that I only get paid for my scheduled shift.
So basically, I pretty much have to work at least a few minutes for free every shift, because I have to be there by or before the start of my shift so I can start work at the scheduled time. And we can get in trouble for being even a couple minutes late if it happens often.
Is this even legal? I mean, it seems like they should have to pay you for all time you work, but I don't know, I'm not a lawyer.
I'm in Illinois, if that matters.