Hi,
I don't think it is too much to worry about, this is a common problem with Fluval filters. With the pipes being corrogated and the actual filter not having much separation for the in/out sections of the filter some particles escape into the out pipe and get stuck in the grooves in the pipe itself. Once you prime the filter after cleaning it blasts air down the tube thus causing all of these bits to come out into the tank.
It can be annoying, especially after you have put fresh clean water into your tank. The best way to stop the particles escaping into the clean water is put a net over the end of the output head and leave it there until you are happy the filter is fully primed then remove it. Some particles will still get past the net but the larger ones that really make a mess should be caught in the net.
Hope this helps, you would think Fluval would of sorted this out by now, it really is a design fault. All other filters I have tried like Aqua one, Eheim, Tetratec all have a clear separation in the filter bucket so that the water being taken in and the water getting pumped out are not able to mix with one another, resulting in clearer water.