The triple and double rolls are independent of each other. The process is important, not just the outcome
It's because they're independant that this works - because 10% of all hits will get the double damage, and that's independant of the triple damage, you can look at cases where you don't get triple and know 10% will get double (so will 10% of cases where you do get triple, but you can ignore those since they're redundant).