I have seen and played non-Alembic basses with those woods in the neck. Padauk has a few different species, and from what I read, vermillion is an alternate name for one of the African species. If you search this site, I'm sure you'll find some instruments made with vermillion as a component of the neck. Vermillion is also used in bodies where the tone it generates seems to be just a little crisper/tighter/punchier than mahogany. My two Alembics both have vermillion cores and the tone is great. As I recall, it also makes a very attractive neck recipe when mixed with maple and purpleheart.
Carvin made a big deal about featuring koa 20 years or so ago and represented an all koa bass as the holy grail of the day. I never bought one, but I saw and played a couple. I can't say that I remember them having any outstanding characteristics that set the tone apart from everything else that was out there. Maybe they were a little warmer than their maple-necked cousins.
Padauk was a component of the neck of a very nice Ibanez that I played back in the early 90s. The SR-1500 was a mostly padauk instrument with EMG guts and was my main bass for a few years. The neck was very thin and shallow, so it moved a bit, but I can't say if this was the fault of the wood or the design. The tone was punchy with nice quick attack, but it didn't have the powerfully tight bottom or sustain of a deluxe Alembic neck. I preferred the tone to most 100% maple necks I have encountered, though.
-bob