Hajj is not obligatory for a person who does ‘Umrah during the months of Hajj

What this person told you is not correct, because Hajj is
only obligatory once in a lifetime, because of the hadeeth of Ibn ‘Abbaas,
which says that al-Aqra’ ibn Haabis asked the Prophet (peace and
blessings of Allaah be upon him): “O Messenger of Allaah, is Hajj (to be
done) every year or only once?” He said: “One once, and whoever does more
than that, it is a voluntary (act of worship).” Narrated by Abu Dawood,
1721; classed as saheeh by al-Albaani. 

Since you did Hajj before that, then you do not have to do
Hajj again. 

There are three months of Hajj: Shawwaal, Dhu’l-Qi’dah and
Dhu’l-Hijjah. Perhaps this person understood from the fact that they are
called the months of Hajj that whoever does ‘Umrah during these months is
obliged to do Hajj. But this is incorrect, rather the reason why they are
called the months of Hajj is that Hajj must happen during these months, not
before or after them. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was
asked about a man who did Hajj tamattu’, then after doing ‘Umrah he went
back to his city and did not do Hajj – does he have to do anything (offer
any expiation or ransom)? 

He replied: You do not have to do anything, because if a
person is doing Hajj tamattu’ and enters ihraam for ‘umrah, then decides not
to do Hajj before he enters ihraam for Hajj, then he does not have to offer
any expiation or ransom, unless he vowed to do Hajj this year. If he made
such a vow then he is obliged to fulfil his vow. 

Fataawa Ibn ‘Uthaymeen, 2/679.