Prices and revenue move in opposite directions does not necessarily mean that the demand is unit elastic. It will be unit elastic if the movement(changes) of 'price' and 'demand' are proportional. But here it is between prices and revenue( price x quantity). Suppose if it is prices increase while revenue decreases, it means that when price increases, the decrease in quantity is greater than the increase in price which only then could causes the revenue to decrease despite the increase in price. Similarly, if it is the case where the price decreases while revenue increases, if the changes in the price and quantity are proportional /equal, the revenue should remain constant. However, if the revenue is suggested to increase when price decreases in this case, the quantity increased should be greater than the decrease in price for the revenue to increase despite the reduce in price.
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