Ambisonics can be rotated with minimal CPU and memory usage by computing rotation matrices in the ambisonic domain. This makes it an ideal format for exchanging audio for VR. For example, you can build a complete auditory scene with sources coming from any direction, encode them to an ambisonics signal, and store it to disk using an ambisonics-capable DAW (such as Wwise). At the moment of playback in the VR device, the playback engine only has to read the head-tracking coordinates, rotate the ambisonics signal in the opposite direction, and then decode/virtualize it to a binaural signal for headphones.
The Using Ambisonics for Head-Mounted Devices section explains how to achieve rotation interactively. You could instead use Wwise to produce non-interactive (cinematic) content for VR, independent of the rotation due to head tracking. To do so, you simply need to replace the aforementioned binaural virtualizer Effect with a Recorder Effect on the ambisonic bus. The recorded file will be a compatible FuMa or AmbiX file, with the same order as that of the bus. You can then embed this file into your 360 video and let the player rotate the sound field using the process described for the head-mounted device.