As I understand it, the timeout period starts as the first probe is sent out. If the probe succeeds right away, the timeout period is over, the pool member is marked as up, and a new generic "interval" period, or an "up" interval if defined, starts.
If the first probe fails right away, a second probe is sent after the defined generic interval; if the first probe hangs, a second probe is also sent after the defined interval period. More probes are sent in this way until the defined timeout period is over, at which time the system will kill all existing connections used by the probes and mark the pool member down.
It would be good if somebody from F5 can confirm / deny this is how it works, and in the latter case, provide a detailed description.