Potential postdoc advisor threatening to fire other postdocs
Can a PI fire a postdoc? 
Surely they can, and sometimes they really have to do so in order to save research money and do the best for the group.
Can PI signal to the postdoc that their performance is under review?
Yes. This is an honest thing to do. It gives postdoc a chance to improve their performance and fix things, before guns will fire.
Is it a good idea to tell this as a joke? 
Absolutely not. The job contract is a serious personal matter. The discussion should be private and professional, not public and semi-serious.
What can we tell about PI's personality?
He cares about the performance of the group and he tries to manage it. He doesn't know/feel what is a professional way of doing it. Perhaps, he struggles to maintain a distance and tends to become a bit too friendly with people in his group. As a result, it is hard for him to communicate difficult decisions and unpleasant messages and he tries to disguise them as a joke.