The moment the rain stopped, the kids ran out the door.
Tips
usage
立时 is a slightly more literary/written-feeling synonym of 立刻 (lìkè) and 立即 (lìjí). All three mean 'immediately', and 立时 is the least common in modern speech — you'll see it more in writing, especially in narrative description.
memory
立 = 'stand / instantly' + 时 = 'time'. 'At the standing time' = right at this moment = immediately.