Sorry for the delay. We've seen this "behavior" quite often in turtles on shore, as they are kind of regurgitating while they rest, and the liquid is colored red. And there are a few instances captured on film where this was seen underwater. However, we are only basing what we think this is from your photos, and the only way to confirm this would be to have the turtle in hand. As you know, this would be difficult, and probably all the stress it would cause the turtle wouldn't be justified. Often, if a turtle is sick or severely injured, it will come ashore and this is the best time to bring them in for evaluation.
As for the side effects for eating so much red algae, there are none directly- algae is the main food source for turtles in Hawaii. Research is underway to determine if toxins or dinoflagellates in or on certain types of algae can be harmful, but nothing is proven beyond a doubt yet.
Hope that helps.