My seeds don't say anything about toasted. They are BLACK, not brown which I would expect with toasted. I have toasted sesame seeds before.
When you add the seeds to cold water they will tend to float. If you stir them, they sink.
I asked much the same question when I started making the tea. Shawn replied that the instructions (removing the floaters) were for a time when getting good quality seeds was harder. This techniques was to clear the poor ones out of your tea. It was no-longer necessary to do the filtering.
Now, I usually short-cut the process and just add hot water to a cup with seeds. I let is seep in the cup, when it's cool enough for me to drink its well seeped.
As an aside in my mental wonderings. Some procedures for making rice involve rinsing the rice first. This does two things. Bits of debri is allowed to float and be removed. This might be part of the process involved in out tea preparation. The second is it reduces the amount of starch in the water (less sticky rice).
You are perfection.
Iam2