Like in the video example, you can correct the offset by fixing the rotation of (in this case) the upper arms after animation is done, with new keyframes. Or you can prevent the problem by setting the rotation axis to X manual. There might be pros and cons with both ways. Illustrations below. You can right click on the images and choose to view in new tab to view large versions.
To get a better understanding of the rolls and rotaion of bones, you can turn on Axes, you'll find that under Armature icon, Object Data Properties, Viewport Display, check the box Axes. When a bone is selected you will be able to se the individual axes, (if you turn on the Wireframe or X-ray, you can see that the Y axis runs along inside the bone from bottom to top).
Notice that the roll of the metarig upper arm and rigigy upper arm differ.
Same goes for DEF-layer
You can change the settings for a bone before you generate a rig. In this case the upper arm of the metarig is selected and under Rigify Type, you can set the Rotation Axis to X manual (instead of Automatic).
The rigify rig upper arm is now similar to the metarig.
