It's almost certain that Hemingway intended for the title of his short story "Soldier's Home" to be ambiguous and to be interpreted in different ways.
The most obvious meaning of the title is that the soldier, in this case, Krebs, is home; that he's arrived home from the...
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war. Here, "soldier's home" is nothing more than a contraction of "The soldier is home."
But on a deeper level, the title refers to a soldier's home, a home for soldiers, a place for former servicemen, many of whom are physically and/or mentally disabled due to their experiences of conflict. A soldier's home would be a place for those without a family or whose health needs are such that they require extensive medical treatment.
Although Krebs, unlike many former servicemen, does have a home and a family, he feels completely estranged from them on returning to his hometown. Mentally, if not physically, he is in a soldier's home, a home for soldiers, separated from his loved ones and the people of his hometown.
By the same token, although he's physically home, physically present in the town of his birth, he doesn't feel as if he belongs there anymore and so cannot reasonably be said to be psychologically present.