The one who is doing Hajj qiraan has to do one tawaaf and one saa‘i

The one who is doing Qiraan, i.e., combining Hajj and ‘Umrah,
only has to do one tawaaf and one saa‘i, like the one who is doing Ifraad
(Hajj only). 

The tawaaf that is obligatory in his case is tawaaf
al-ifaadah. With regard to tawaaf al-qudoom, it is Sunnah. In his case,
saa‘i may be done after tawaaf al-qudoom, or he may delay it and do it after
tawaaf al-ifaadah. 

This is what is indicated by the saheeh Sunnah and is the
view of most of the scholars. 

Ibn Qudaamah (may Allah have mercy on him) said: The well
known view narrated from Ahmad is that the one who is doing qiraan, i.e.,
combining Hajj and ‘Umrah, does not have to any actions but those that are
required of the one who is doing ifraad (Hajj only), and one tawaaf and one
saa‘i are acceptable in his case, for both his Hajj and his ‘Umrah. This is
the view of Ibn ‘Umar and Jaabir ibn ‘Abdullah, and was also suggested by
‘Ata’, Tawoos, Mujaahid, Maalik, ash-Shaafa‘i, Ishaaq, Abu Thawr and Ibn al-Mundhir. 

Another report was narrated from Ahmad, which suggests that
he has to do two tawaafs and two saa‘is. This was the view of ath-Thawri and
Abu Haneefah, and was also narrated from ‘Ali, but the report from him is
not saheeh. 

Then he quoted the evidence of the majority and said: It was
narrated from ‘Aa’ishah (may Allah be pleased with her) that she said: As
for those who combined Hajj and ‘Umrah, rather they only did one tawaaf for
both. Agreed upon. In Muslim it is narrated that the Prophet (blessings and
peace of Allah be upon him) said to ‘Aa’ishah, when she did Hajj and ‘Umrah
together (qiraan): Your tawaaf is enough for your Hajj and ‘Umrah.”  

It was narrated that Ibn ‘Umar said: The Messenger of Allah
(blessings and peace of Allah be upon him) said: “Whoever enters ihram for
Hajj and ‘Umrah (combined), one tawaaf and one saa‘i is sufficient for
both.” It was narrated from Jaabir that the Prophet (blessing and peace of
Allah be upon him) combined Hajj and ‘Umrah (qiraan) and did one tawaaf for
both. These two reports were narrated by at-Tirmidhi, who said concerning
each of them: a hasan hadeeth. Ibn Maajah narrated from Jaabir, Ibn ‘Umar
and Ibn ‘Abbaas that the Messenger of Allah (blessing and peace of Allah be
upon him) and his Companions only did one tawaaf for their ‘Umrah and Hajj.
End quote from al-Mughni, 3/241 

Shaykh Muhammad al-Ameen ash-Shanqeeti (may Allah have mercy
on him) said: The majority of scholars who differentiate between qiraan and
tamattu‘ say that for the one who is doing qiraan, one tawaaf is sufficient
for both his Hajj and ‘Umrah, and that is tawaaf al-ifaadah, and one saa‘i.
They quoted as evidence saheeh hadeeths, which cannot be matched by those
who differ from them. 

End quote from Adwa’ al-Bayaan,
4/430 

Thus it becomes clear that what you were told about the one
who is doing qiraan of having to do one saa‘i is the correct view. 

It is quite clear that when the one who is doing qiraan has
done tawaaf upon arrival (tawaaf al-qudoom) and saa‘i, he then remains in
his ihram and does not remove any of his hair and does not call what he has
done ‘Umrah; rather it is part of the actions of Hajj and ‘Umrah combined. 

And Allah knows best.