I was referring to deepceleron's post, not bb's, and addressing bb not deepceleron. I know what he and you did was correct and the procedure to create a random number that will be distributed according to the poisson process is well known. i apologise for the confusion.
That makes some sense, except that if you read deepceleron's post you'll see it's correct too and is basically the same as what I wrote. You draw the
percentile uniformly in [0,1], and translate it to a value using the inverse of the cumulative distribution function (log in our case).