This is not correct. The Bemba and Bisa came from the Luba Empire. I need to re-research.
This map is from Marvin Miracle’s book from 1963. It shows the distribution of the tribes at this time.

The following information comes from Marvin Miracle’s article on ‘Migration of the Northern Rhodesian Senga’, published in 1963.
It would seem that the Senga, Bisa and Bemba all left the Lunda empire during the reign of a particularly bad king, Mwata Yamvo. The Lunda king had his palace at a place called Uluwa.
Family clans under Lunda government were given one particular task to carry out. The Bemba were part of the Nandu or crocodile clan whose duty was to sweep the royal village. The Bisa (Ngona or mushroom) clan were tasked with preparing millet for the royal brew. It is not known what duties were allocated to the Senga clan.
According to the opinion of Marvin Miracle the Senga left the Lunda Empire first. Their planning to leave took several years but eventually, one night, the men fled and travelled east. During their migration they stopped for a long time and it was during this time that the Bemba and Bisa clans also fled the Lunda Empire. When the Senga continued their migration east, they came to meet up with the Bisa who had settled there.
The date of the Senga fleeing the Lunda Empire is not clear but it is estimated to be around 1700 AD. The leaders of this migration were Chibeza Kambombo, Kampate Tembwe and Kamponje Lundu.
An interesting story from this migration is about Mulopwe, one of the chief advisors who was also the ‘bearer of seeds’. The seeds were carried in his hair. These seeds would have been vital for new gardens at the end of their migration.
The Senga reached Mphalakasanga Hill where they hoped to settle but found that food was not plentiful so they moved on to a place called Masipi Pool. It is here that the clan separated into the Senga and Nsenga clans. Chibeza Kambombo, Kampata Tembwe and Kamaponje Lundu continued east, leaving behind Maole Chikwa and Kasusulu Chifunda. (The latter finally gave up waiting for a message from the first group and left Masipi Pool to travel south to find a new home and become the Nsenga).
The Senga clan reached Chief Kopa of the Bisa people and stayed there a while. The Senga were apparently excellent dancers and caused jealousy among the Bisa so eventually the Senga decided to move on before this jealousy led to something more serious.
Passing through another Bisa territory headed by Chibeza-Kunda, the Senga continued their migration to Panombwe Hill where Kamaponje and his family decided to stay. Chibeza Kambombo and Kampata Tembwe continued east into the Luangwa Valley. They settled at first on the east of the Luangwa River but then left for twin peaks they could see in the distance – Mparausenga Hill. They found the area fertile and largely uninhabited. The only occupants of the area were Tumbuka hunters. The Tumbuka hunters killed elephant for food and had no idea of the value of the tusks for trade, using them to sit on or to hold up their cooking pots.
This Senga clan acquired a new name at this point. They tried to climb to the top of Mparausenga Hill and failed. In the language of the Tumbuka, to fail to climb a hill is ‘tagoma’, so from that time the clan was known as the Goma clan.
The Senga clan, it is thought had no women in its group so the men had to do all the work including pounding the meal and cooking food. The name of their first village was named Chipulabalume, meaning in the Tumbuka language, ‘the men who pound’.
After a while the clan again split with the family of Kampata Tembwe moved further south to set up his own village.
Both these clans of Senga people prospered. The land was good and through the Tumbuka they exploited the trade in elephant tusks. The Tumbuka had elephant tusks littering their villages and after collecting them, the Senga sent them east and traded them for cloth, beads, etc, thereby becoming rich and powerful. They also claimed that the Tumbuka were now under their authority as a tribute clan.