But if every change in the past fractures the timeline into new ones, with the number of travelers you'd have 100's or 1000's of timelines, each with their own Director and time travel equipment. And you'd probably start to see duplicate travelers sent back, because in a future timeline perhaps they didn't send the same guy at the same time, so you'd see copies coming at different times.
If they all come to the same "present" timeline, things would get well and truly fucked real quick. The only way such a premise works is if you have one future timeline and one present timeline, or if a timeline fracture occurs it fractures both the present and future together so that any action by that future occurs in the present that it is associated with. It's really a complicated issue, made more complicated by the fact that it's impossible and we have no idea what'd actually happen...
They mention that due to the tech they can only go back as far as the last person they sent. That means the present time is always happening in a fixed order and not being revised.
There's actually reasonably good indications that what the present timeline is getting fucked up by people from all different future timelines showing up with conflicting orders and 'things getting fucked real quick' pretty much sums it up ;p