After days of speculation, Massimo Ficcadenti parted company with the club for a second time after failing to deliver a victory in six attempts this season.
Pulga, a firm fan favourite in Sardinia, was part of the side that won successive promotions to the top flight under Claudio Ranieri in the 1980s.
But reports in Italy have suggested that his assistant Diego Lopez is Ficcadenti's true successor, with Pulga installed to keep the bench warm while the Uruguayan earns his coaching licence.
Pulga gave that idea short-shrift, though, insisting that he is very much in charge of Cagliari's destiny, starting with Sunday's trip to Torino.
He told Gazzetta.it: "Like with all partnerships, we'll argue, we'll debate and we'll make decisions together, but I'll have the last word.
"It's always been my dream to come back and work here and it fills me with joy that my dream has come true.
"Our main objective is to stay up. And then I'd like to stay on for another six years, like when I was a player here.
"Cagliari has a good structure, we're not here to revolutionise the club. You'll see what tactics we employ on Sunday, but for now, I'm saying nothing.
"We need to lift the depression from our players so we can start getting results, but Ficcadenti left the team in decent shape."
Pulga has a good idea of what kind of side the Isolani will face at the Stadio Olimpico, having worked as a travelling club scout before returning to Cagliari.
He added: "I know them well, when I was working for Modena I watched them seven or eight times and they haven't changed much since then."
Talismanic striker Rolando Bianchi led Torino's uncompromising 5-1 victory at Atalanta on Sunday, and Granata boss Giampiero Ventura wants to see a similar level of commitment across his entire team.
"We are a group, a united and cohesive group, and that is where our strength lies," Ventura told Gazzetta.it.
"The power we derived from the shirt was our strength in Serie B, and so it will be in Serie A."