Wrong.
Both entered around the same time, zero evidence for a second migration.
First "T" migration at 23 kya enters the central Sahara and is included in all of E1b1b. . Second migration at 6-8 kya to 3 kya (likely from a Neolithic migration into the Red Sea Hills) forms the "T" clans in the north. E1b1b-V32 (52% of all Somalis) comes up the Nile and enters Somalia from the south and west.
Here is the second "T" migration:
https://www.eupedia.com/europe/Haplogroup_T_Y-DNA.shtml
"The higher frequency of T in
East Africa would be due to a
founder effect among Neolithic farmers or pastoralists from the Middle East. One theory is that haplogroup T spread alongside
J1 as herder-hunters in the Pre-Pottery Neolithic period, leaving the Zagros mountains between 9,000 and 10,000 BCE, reaching the Egypt and the southern Arabian peninsula around 7,000 BCE, then propagating from there to the Horn of Africa, and later on to Madagascar. However, considering that J1 peaks in Yemen and Sudan, while T1 is most common in southern Egypt, Eritrea and Somalia, the two may not necessarily have spread together. They might instead have spread as separate nomadic tribes of herders who colonised the Red Sea region during the Neolithic, a period than spanned over several millennia. Nevertheless both are found in all the Arabian peninsula, all the way from Egypt to Somalia, and in Madagascar. This contrasts with other Near Eastern haplogroups like G2a and J2, which are conspicuously absent from East Africa, and rare in the Arabian peninsula. Nowadays, T1a subclades dating from the Neolithic found in East Africa include Y16247 (downstream of CTS2214) and Y16897. Other subclades dating from the Bronze Age (see below) are present as well, such as Y15711 and Y21004, both downstream of CTS2214."