I have been observing that Process.HasExited sometimes returns true even though the process is still running.
My code below starts a proces
So just for a further investigation into the root cause of the problem you should maybe check out what's really happening by using Process Monitor. Simply start it and include the external program and your own tool and let it record what happens.
Within the log you should see how the external tool writes to the output file and how you open that file. But within this log you should see in which order all these accesses happen.
The first thing that came to my mind is that the Process class doesn't lie and the process is really gone when it tells so. So problem is that at this point in time it seems that the file is still not fully available. I think this is a problem of the OS, cause it holds some parts of the file still within a cache that is not fully written onto the disk and the tool has simply exited itself without flushing its file handles.
With this in mind you should see within the log that the external tool created the file, exited and AFTER that the file will be flushed/closed (by the OS [maybe remove any filters when you found this point within the log]).
So if my assumptions are correct the root cause would be the bad behavior of your external tool which you can't change thus leading to simply wait a little bit after the process has exited and hope that the timeout is long enough to get the file flushed/closed by the OS (maybe try to open the file in a loop with a timeout till it succeeded).