That first sign ("begins") is to inform road users that the center lane acts as a left turn lane for traffic in both directions and to be aware of oncoming vehicles in that lane if you're using it. The second sign ("ends") is telling you that the shared center turn lane has ended.
It has nothing to do with the traffic islands, nor the designated left turn lane down at the intersection.
The issue is not with the two-way left turn lane signs. The issue is that at the end of the lane, the black and yellow obstruction sign is upside down. In HB's video, the black lines are angled to the left. That means "keep left of the obstruction". So the sign is telling motorists to go into oncoming traffic to go around the island. In the Google Maps image that I then posted, you can see the correct alignment of the obstruction sign, with the black lines angled to the right, meaning "keep right of the obstruction", and sending motorists back into the correct traffic lane.