After Luca threatened to take everything into his own hands, Miss Marcaida had to respond quickly and cut a deal with the alpha or she knew he would do something.
The press conference was mostly improvised but he still did everything she advised him to. He needed to admit his guilt and turn himself in. For weeks he had been restructuring Falcone Investments and Holdings so there were plenty below him who could step in while he was out.
Since he hadn't been officially charged with anything, he was still technically the CEO. The jail he was in had to permit at least a little bit of communication between him and his office in case something happened in his absence. Luckily, it seemed he had done a good job so far and things were running smoothly even without him there.
Other than stock prices dropping, Luca had already cashed out so he wasn't seeing the implications of turning himself in.