Total emissions can rise, even though the emissions per dollar declines. Emissions per dollar is a relative term which is calculated by dividing the total emissions by the GDP ($). If the GDP rises much faster than the amount of emissions, then, the emissions per dollar will decrease, because the denominator in the formula is increasing faster than the numerator.
The total emissions is an absolute term, which is cumulative as the the amount of emissions increases. As an example, consider the emissions per dollar changing from 2/3 (0.667) to 5/8 (0.625). The numerator increased from 2 to 5, whereas the denominator increased from 3 to 8. Generally, in most economic issues, relative terms are very important for economic evaluation and decision-making by government, but in environmental issues like emissions, the absolute values are equally important.