Wood is always working. Even if you plane a board and leave it in a room overnight, it might warp. There's really no way you can avoid that in principle after a piece has been finished. (Now, this particular board should do a bit better than sawn wood, since it is glued, although it does not seem as if special care has been taken to orient the growth directions alternatingly, which is what you should do in such a case. An even better solution would be to put orthogonal strips onto the end-grain with a tongue and groove.)
Anyway, that's likely not really bad in your situation. Since the wood is always working, it doesn't have to stay that way: maybe it's just wet now and will warp back in a couple of hours or days. In my experience, you can sometimes speed up things by trying to dry the piece evenly (for example, by leaving it in some dry place with a gap underneath to let the air through), re-wetting it on one side, and letting it dry again. And when you have a board for some time, you'll know how it reacts.
The oiling is a good idea for the surface but does not help very much with warping. What does help is to keep moisture always even: when you wash or wipe the board: do so on both sides. When you dry it: keep moisture and temperature the same on both sides (e.g., avoid standing it up next to your oven or something like that). That means you can submerse it (and should even do so, to wash it) -- just don't let it stand in water, and wash it from all sides equally. Avoid drying in an oven or other drastic temperature changes.
One thing you really want to watch out for, though, is splitting between the individual strips, which can happen due to the stress of repeated warping. In that case, there's little left you can do (save shortening the board). A split is not technically problematic (the whole thing will still be stable), but the groove can collect nasty stuff (still OK for cutting bread, though). Quality boards, specifically made for kitchen use, will be less prone to this, though.