Apparently these are UAE-backed militias. The UAE is apparently more willing to reach a peace agreement with the Houthis than the Saudis are. The UAE-backed militias have attacked the Saudi-backed Hadi government forces, sometimes with direct UAE air support.
AP reported at the beginning of September:
Last week saw a stunning escalation in the turmoil in the south, as Emirati warplanes blasted fighters loyal to Yemen’s internationally recognized president, Abed Rabbo Mansour Hadi — the man the coalition is supposed to be trying to restore to power. Dozens were killed, and the UAE rubbed salt in the wound by calling Hadi’s forces “terrorists.”
Hadi’s loyalists call the strike a “turning point” and accuse the UAE of fomenting a coup by its allied militias to topple his government and seek secession in the south.
In August, the militias overran Aden and other southern cities, driving out Hadi’s forces in bloody fighting. When they tried to expand into oil-rich Shabwa province, the Saudis rushed supplies to Hadi’s forces to drive them back. [...]
The militias were driven back. Hadi’s forces began a countermarch, advancing to the gates of Aden — despite private Saudi warnings for them not to escalate by entering the city or approaching its airport. There they were hit by Emirati airstrikes on Aug. 29, killing at least 30 fighters and leaving a trail of burned-out vehicles.
The UAE dominates the south through the militias it arms and finances, which run bases and authorities independent of the government. In 2017, the militias integrated under the Southern Transitional Council, or STC, which seeks the return of the independent state that existed in the south until 1990.
In the new eruption of violence, the STC denies it seeks immediate secession or Hadi’s removal. But it demands the purge of “terrorists” it says have allied with Hadi, referring to the Muslim Brotherhood’s Yemeni arm, known as the Islah Party.
Also, according to that report, in order to facilitate a peace deal with the Houthis, the UAE withdrew its ground forces from Yemen without giving the Saudis any advance warning.
Saudi Arabia also conducted some air strikes against STC forces on Aug 11, during the STC takeover of Aden.
The STC seem to be really uncomfortable with the postion in the Hadi government of Ali Mohsen al-Ahmar:
Ali Mohsen was the former commander of the northwestern military district and 1st Armored Division, having helped crush southern forces during the North-South civil war and led the Saada wars against the Houthis. Ali Mohsen is from Saleh’s Sanhan clan and is closely aligned with Islah. Mohsen also has a storied history of helping spread Salafist/Wahabi teachings and recruiting mujahideen to fight in Afghanistan, including Tariq al-Fadhli (Ali Mohsen’s brother-in-law), who helped found the Islamic Jihad Movement and allegedly helped assassinate southern leaders. Ali Mohsen’s partnership with Hadi came with a price—the position of deputy supreme commander of the military and then vice president—but he delivered highly essential military units and brought with him a host of Islah-aligned militias and supporters.
The problem with Ali Mohsen once again being in a position of power is multifaceted. The memory of the civil war is a significant motivation for secessionist sentiment and Ali Mohsen is viewed as the face of the North’s destruction of the South during the civil war. Mohsen has long been accused of ties to al-Qaeda in the Arabian Peninsula and was previously accused of facilitating the assassination of secessionist leaders. Ali Mohsen is also a prominent Islah-affiliated figure, which has long been at odds with Southern secessionist groups as well as the Emiratis.
There was a reconciliation announced on 25 Oct 2019. Basically, the Hadi government now officially shares power with the STC:
The newly negotiated government will involve a 24-member government with an equal number of ministries allocated to the STC and Hadi supporters.
The deal is a significant enhancement of the status of the STC, which has previously been excluded from all UN-brokered peace deals, and STC sources appeared to be more pleased with the agreement than the other side.
Although the UAE-backed STC won political concessions, on the ground the Saudi military replaced the UAE one in STC strongholds:
In preparation for the agreement Saudi forces have already moved into Aden and key military bases, replacing departing UAE troops.