Why don't effervescent vitamin C tablets react with the vitamin C?
Acid-base reactions are fast and reversible (barring any additional reaction that occurs). That is, once you move the conjugate base of ascorbic acid to a low-pH environment (e.g. your stomach), it rapidly reverts to the protonated form. (Ascorbic acid does not undergo any pH-dependent further reactions, as opposed to carbonate, which when protonated to carbonic acid can decompose to carbon dioxide and water.)

Actually, as the pKa (roughly the "halfway pH" of acid/base reactions) of ascorbic acid is 4.2, the moment the protonated ascorbic acid enters your bloodstream (roughly pH 7.3), it immediately loses that proton again, reverting to the deprotonated ascorbate ion.

So in a practical sense, it really doesn't matter which form you take your Vitamin C in - either (protonated) ascorbic acid or (deprotonated) ascorbate acts in you body the same way, because they can rapidly interconvert based on the pH of the solution they happen to be in at the time. 

(Because they typically work in buffered aqueous environments, biochemists typically play fast-and-loose with the difference between the protonation states of molecules. Unless you're explicitly dealing with pH-dependance, they're typically lumped all together, with the implicit understanding that at a given pH they'll adjust to the appropriate relative concentration. This can get confusing if you're a stickler for nomenclature.)