The Blues sacked Tuchel on September 7 following a 1-0 defeat to Dinamo Zagreb in the UEFA Champions League.
This was despite the German leading Chelsea to their second Champions League in 2021 and the UEFA Super Cup and FIFA Club World Cup in 2022.
Boehly purchased the west London club from Roman Abramovich in May and had only been owner of the Blues for four months before dismissing Tuchel.
There have been debates over Boehly's decision, and Aulas has taken a shot at the American billionaire.
Lyon are currently seventh in the Ligue 1 table with four wins, as many defeats and one draw in nine games.
Touching on the Ligue 1 side's recent poor form with regard to whether he would consider sacking manager Peter Bosz, Aulas said:
"I’m not here to start a revolution. I am not a billionaire (Boehly) who sacks someone who won the Champions League (Tuchel) as Chelsea did. I make decisions primarily in the interest of the club, and he (Bosz) will stay."
Chelsea were sitting in sixth when Boehly decided to dismiss Tuchel before replacing him with Brighton & Hove Albion coach Graham Potter on September 9.
They had won three, drawn one and lost two of their seven league fixtures alongside the defeat to Zagreb in Europe's elite club competition.
Boehly defended his decision to part ways with Tuchel, saying:
"Tuchel is extremely talented and had great success, our vision for the club was finding a manager that wanted to collaborate with us.”
“But we weren’t sure Thomas saw our vision the same way we saw it, we didn’t have a shared vision.”
Potter is a long-term appointment at Chelsea
Potter succeeded Tuchel just two days after the German was sacked and he was handed a five-year deal at Stamford Bridge.
Boehly's vision is clear in that he wants to a long-term project to be seen out at Chelsea, and Potter fits the bill.
His work at Brighton has drawn huge acclaim as he transformed them into one of the Premier League's most exciting teams to watch on a low budget.
The Seagulls have progressively moved up the league table season after season under his tenure and Potter had them sitting in fourth before he parted.
The focus now is on the English coach putting his imprint on the Blues, with regards to playing style and building his own team.
The English coach has overseen a 1-1 draw with RB Salzburg in the Champions League and 2-1 win over Crystal Palace in the Premier League so far in his tenure in charge.