Confidence interval means that is expected conversion rate of A is 0.5 and for B is 0.4, what is the actual spread. In other words, say, for 95% of the time does the conversion rate fall in the 0.3-0.5 range or 0.35-0.45 range. More data you collect , narrower this range will be. Confidence bounds for individual conversion rates can be calculated from the formula since they follow beta distribution. What Evan is saying that the confidence bound for the difference in conversion rates would need to be calculated through repeated simulations and taking (say) 5 percentile and 95 percentile of the values that come.
For example, given you know probabilities for A and B (say 0.5 and 0.4) and that number of trials has been 100, you can simply run thousands of simulations, know what the conversion rates come out to be in respective simulations and aggregate the difference in conversion rates at the end of each simulation. That would be a confidence bound.