It might not be what you want but what I see in the video looks correct to me...well, technically, anyway.
A group layer always has a minimum bounding region around its origin, which is why the bounding box appears offset to the left of the origin. When you add an item to the group, the group's bounding box expands to accommodate the new item's bounding region but it still maintains some of the group's bounding box around its origin, which is why it looks 'offset' (it's not really.)
If you want to have the bounding box accommodate
only the child items, you need to move the group's origin over the items. You can use the Set Origin tool for this, and this is only necessary if you intend to transform the group around that origin. If you ever need to reset the Group or Layer origin back to 0,0, use the tool's Reset button.
In general, it's best to draw your items in place with all the layers set in XYZ position to 0,0,0. Transforming the layers during animation is fine but when setting up and rigging on frame 0, it's good practice to keep as the layer positions at 0,0,0, rotation at 0, and scale at 1.0...this can prevent any unwanted surprises later on. If you already drew the items in offset positions, you can transform them to the correct positions using the Transform Points tool instead of Transform Layer. This doesn't mean you can't use Transform Layer at frame 0 but you should be aware of the potential consequences when you do.
As for intentionally offsetting the origin for a group, you should have a good reason for doing this too. I sometimes do this when I have a master parent group that I wish to use for squash and stretch as a character performs or walks, and in this situation I typically place the group origin at the feet of the character.
Hope this helps.