To my knowledge, when an item rolls, it will roll whether it's ilvl 61, 62, or 63, then it will roll affixes according to the level of the monster that drops it (ie. lvl 63 for mp1+). For example, a doom armor and an archon armor dropping from the same monster can roll the same affixes, but the doom armor will have less base armor because it's a doom armor (duh).
Now, I have a question about off-hand items (source and mojo). Does the damage linked to its item level or monster level. For example, should I bother picking up non-62 mojos and sources because they can't have as high dmg as a 62-ones? Or is the dmg related to the monster level and all sources can roll the same dmg?
Since its kinda impossible to sell even a realy good rolled rare source/mojo i dont bother picking em up. But to answer your question. AFAIK the damage range is still based on itemlevel and not the monsterlevel who droped the item. Never saw an ilv60/61 with nearly high avg. dmg like a 62 rare.
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Words of wisdom: Don't follow the advice of people who won't have to deal with the consequences.
This should be pretty easy to check in the AH. Narrow your search to Off hand Mojo or Source and put in your only search parameter as "average damage" and then sort the results by damage and see what the best ones are. If the first pages are all 62/63s then you know that it's set on item level.
I'd be curious to know this as well, so maybe you can post your findings? I'm not near a computer I can access D3 from, so I can't do this myself...