Both these men know each other well.
Koeman was a hard-nosed, tough player mentally. He once traded his shirt with opponent Olaf Thon only to admit he'd wiped his ass with it. It became a minor scandal. Later on he sang the cirtues of a two-footed crunching tackle as "beautiful", which was not received well either. It was a minor miracle that as a player he reached the absolute top since he was always the slowest player on the pitch, which speaks for his tactical nous and concentration.
As a trainer he has been developing steadily. Van Gaal butted heads with him at Ajax when van Gaal was technical director and Koeman trainer, especially over Zlatan. Van Gaal overstepped his bounds when he explained to Zlatan how a number 9 should move, and both Zlatan and Koeman were not amused.
As a trainer, Koeman is a practical coach who is good at setting up a defence and in a natural way demands respect in a dressing room. At Ajax, his door was always open, but the only player who regularly dared to step through it was Wesley Sneijder.
Van Gaal is as a coach more special, with a more idealistic view, but there is no one Koeman wants to beat more.
We can expect Southampton to go all-out. If they play for their trainer, this is a cupfinal for them.