With the new DLC Captain Scarlett and her pirate's booty, they're adding new weapons and stuffs. Does this mean that new loots are only spawning in those new areas or could be spawning anywhere else?
Yes, they do.
The only new weapons/equipment in Captain Scarlett's DLC are quest rewards and Seraph weapons, only purchasable from a shop inside the DLC. None of the new items are available outside the DLC, though if you get the items you can take them outside the DLC zone.
Source: we beat it the first day it was released. There appears to be no new chest-based/normal loot whatsoever. In addition I'm not sure if there are any rare drops, but there definitely are unique (blue) gun drops from several bosses in the DLC (and nowhere else, like other unique guns). Additionally this is exactly how DLC worked in Borderlands 1.