My condescending tone comes out when someone is trying to spread incorrect information while stubbornly asserting that they're right.
I'm very familiar with DoT mechanics. Yes recasting a DoT before the current one has expired will add that tick onto the new one, it's been that way for years now. In the case of Pre-5.0 DP and Post-5.0 SW:P the damage on cast means that if you refresh immediately after a tick you will gain almost a full extra tick's worth of damage in that same window of time over if you just refreshed before a tick.
Shadowpriest.com is gone now (RIP good buddy!) but the new Shadowpriest.com is Veiled's HowToPriest.com (You really must check it out, it's quite awesome). Over there you can read through the threads and you may even stumble upon my little guide
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... if your DoT uptime was 2ms less but you got almost a full extra tick's worth of damage in that same window of time over if you just refreshed before a tick you would call that DPS loss? How... Wha... I don't even.
See above for the answer to DP.
More damage in the same amount of time = higher DPS
If you all are still having trouble with this imagine a time line in your head where all the DoT ticks are mapped out. Don't make me break out some terribly laughable MS Paint picture on you!