The deuterium exchange is simply telling you the deprotonation (and protonation) step is faster than the elimination. If that were not the case, no deuterium would be incorporated as every anion would result in elimination. That is not happening. Therefore, the reaction rate is first order in the benzylic anion, hence E1cb.
Although textbooks refer to concerted reactions, a closer look would show that reactions may have varying degrees of bond formation and breakage. A good example is Hofmann and Saytzev eliminations. Hofmann elimination are more E1cb-like and eliminate from the most acidic proton while Saytzev eliminations are more E1-like and result if loss of a proton from the most substituted carbon, or carbocation-like.