Do I need to do anything for the temporary promotion while deployed if I've made the cutoff score points? Or will it be automatic?

Check HRC website

The info for the temporary promotions is on the HRC enlisted promotions website

It may very well be automatic. But the "automaticity" depends on your milpo or PAC clerk doing his/her/its job. As well as your branch mgr doing his part etc. So you can assume that so many others are competent at their job. But would you want to leave your promotion to chance? Rely on an assumption. Assuming others are competent or that they care about your career progression is not realistic.