Specifically if you are using an Atomos recorder, or any recorder that supports the Atomos open protocol, you'll be able to hit record on the camera to trigger the recorder. Here's more on that:

 An External recording control option has been added to the HDMI item in the SETUP MENU. If the camera is connected via HDMI to a third-party recorder that supports the Atomos Open Protocol (the Atomos SHOGUN, NINJA2, or NINJA BLADE), selecting On allows camera controls to be used to start and stop recording. More information is available in a supplementary manual.
Note: Choose an option other than 576p (progressive) or 480p (progressive) for HDMI > Output resolution in the SETUP MENU.

This option was already available in other cameras like the D810, but it's nice to see it on other options in Nikon's lineup. I've always preferred using a physical button to record rather than hitting a fake button on a touchscreen, especially as you sometimes might not press hard enough on the screen to actually start the recording.

A number of other fixes have been implemented in these firmware updates, and you can find the D4S 1.30 firmware available here, and the D750 1.10 firmware available here

Nikon D4S 1.30 Firmware Update

Nikon D750 1.10 Firmware Update