First of all, Vietnam was devided in 1954 due to the Geneva-Conference which ended the first Indochina-War
https://en.wikipedia.org/wiki/1954_Geneva_Conference
https://en.wikipedia.org/wiki/1954_Geneva_Conference#Provisions
https://en.wikipedia.org/wiki/State_of_Vietnam_referendum,_1955
The French-backed
State of Vietnam, led by former Emperor
Bảo Đại, provisionally held control south of the 17th parallel.
Hồ Chí Minh's
Viet Minh held the north under the
Democratic Republic of Vietnam, which Hồ Chí Minh had proclaimed in 1945. The agreements stated that nationwide elections were to be held in 1956 to unify the country under a common government.
It was clear to all that the Vietminh would probably win those elections planned for 1956. So, Diem had a "Referendum" in 1955 and tereafter formed the Republic of Vietnam.
The "Referendum" was a total fraud
Though published counts showed Diệm winning the election with 98.2% of the vote, the referendum was widely marred by
electoral fraud. In the capital,
Saigon, Diệm was credited with more than 600,000 votes, although only 450,000 people were on the electoral roll.
[1][2] He accumulated tallies in excess of 90% of the registered voters, even in rural regions where opposition groups prevented voting.
But, North Vietnam had no territory to reclaim in the South, since it never had legal control over vietnamese territory South of the 17th parallel in the first Place.
The failure of reunification led to the creation of the
National Liberation Front (better known as the Viet Cong) by Ho Chi Minh's government. They were closely aided by the
Vietnam People's Army (VPA) of the North, also known as the
North Vietnamese Army. The result was the
Vietnam War.
So, the presence of NVA-troops on South vietnamese soil was not justified. The US presence, on the other hand, was justified since the South vietnamese goverment had invited the US forces ( same as with russian troops in Syria today).
The US presence was legal, the North Vietnamese presence illegal.