Does the pilgrim performing Tamattu's stay in Jeddah for two days for work and to run errands change the type of his Hajj, given that he arrived in Makkah to perform 'Umrah with the intention of Tamattu', and then returned to Jeddah due to work?

Whoever performs Umrah during the months of Hajj and then performs Hajj in the same year is considered a Mutamatti (one performing Tamattu Hajj), unless he travels to his homeland between Hajj and Umrah, which would sever his Tamattu. If he then enters into ihram for Hajj, he would be performing Ifraad (Hajj only). If he wishes to perform Tamattu, he must enter into ihram for Umrah once again before Hajj.

When a Mutamatti enters into ihram and arrives in Makkah, he may perform tawaf, sai, and shorten his hair, thus exiting his Umrah ihram. He is permitted to travel to Jeddah, Ta'if, Madinah, or other cities, and his Tamattu status will not be severed, even if he returns in ihram for Hajj. However, if he travels to his homeland and then returns in ihram for Hajj, his Tamattu status is severed, and he becomes a Mufrid (one performing Ifraad Hajj). If he returns in ihram for Umrah after returning to his homeland, he becomes a Mutamatti with the second Umrah.

Ibn Baz clarified that whoever performs Umrah in Shawwal, then returns to his family, and then performs Hajj as a Mufrid, the majority opinion is that he is not a Mutamatti and is not required to offer a sacrifice (hady). This is narrated from Umar and his son. However, whoever comes for Hajj and performs Umrah, then remains in Jeddah or Ta'if, and is not from their residents, and then enters into ihram for Hajj, this person is a Mutamatti and must offer the Tamattu sacrifice.

A Mutamatti's travel to Jeddah (his hometown) severs his Tamattu. If you intend to perform Tamattu, perform Umrah before Hajj, and do not return to Jeddah thereafter until you perform Hajj.