A developer said to me: developers may hurry to finish the project before deadline that they might miss many security bugs specially in the updates. That a creative hacker will later take his time and exploit them.

Is it correct ?

Yes

or PM's hurry devs and when they raise their concerns about possible bugs and sec issues some PM's still insist on the quickest delivery and don't give a fuck about anything else

Yes. The biggest source of buggery is rushing through a project using worst practices to "get 'er done" without paying attention to security best practices. The end result is that instead of saving time and money, it costs more tone and money, often by huge factors.