From Shrimad Bhagvat, 8th Skandh,
King Parikshit askes Shukdevji, how did Bali became so powerful?
Shukdevji's answer was, after Samudra manthan, in Devasur war, Indra defeated Bali, took away all his wealth, killed him with Vajra. At that time Bhrigu's son Shukracharya, brought him back to life with his Sanjeevani Vidya. Bali gave whatever he had to Shukracharya & started serving all Bhriguvanshi Brhamins. Pleased with his sewa, they all made him perform Vishwajeet yagya to win over Swarga. From the yagya kunda, a golden Chariot, Green Horse like Indra's, a flag with Lion's sign, a divine bow with arrows, a shield appeared. His grand father Prahlad presented him a garland, Shukrachaya gave a counch to Bali. After receiving them Bali discussed with Prahlad, took his & the Brahmin's blessings, moved over to Amaravati 'Swarga with his army.
Seeing him well prepared, Indra got scared, asked Brihaspati, I won't be able to defeat him this time, how did he become so powerful? Brihaspati answered, Bhriguvanshi Brahmins have made him so powerful, except God, no one can stand in front of him. It's better you all leave Swarga & hide somewhere, the day Bali disrespects Brahmins, at that time he will get destroyed. Indra with other Devas did the same, so Virochan's son Bali, took over Swarga & 3 lokas.
This indicates Bali who is shown in the show is Prahlad's grandson & Virochan's son Bali. He was Asura's leader during Samudra Manthan, not some other Bali.