The video shows Ulis holding an elevator door for his friends, at which point a group of men confronted him and things turned physical.
"When Tyler tried to block them ... they took offense and a scuffle broke out," TMZ wrote. "One guy grabbed Tyler while another man put him in a headlock. The fight spilled out of the elevator and into the hallway."
Devin Booker can be seen later in the video riding the elevator to the scene of the fight. Upon arrival, he intervenes but does not appear to throw any punches.
The Suns waived Ulis shortly before the start of free agency. According to Yahoo Sports' Shams Charania, Booker was "upset" the front office decided to cut his best friend.
Booker and the Suns have since agreed to a five-year, $158 million contract extension.
"I am humbled & honored to commit to the Suns organization long term," Booker wrote after signing his new deal. "I loved calling Phoenix home the last 3 seasons as this team & community are special to me. Thank you to the Suns for drafting me and believing in me. I look forward to the future & pursuing a title as a Sun."