You don't really need to seal it entirely. Could you take a closer pic please? If you're worried, you could just dip your seeds in a very weak bleach 1 to 10 bleach to water. I can't really see if the seeds are germinating. Sometimes, the skin colour of the seeds might look black. It might not be all dead. Try some more. The method certainly works. My only concern is when you have about 6 in one towel, the roots will mat together and you can't really plant 6 seedlings in a pot as you will have a lot of competition. I have seen the black colour quite a few times. It is a good method as I found out that I was sold dead woodchips instead of clematis when I trialled the method.
Don't worry too much about the colour. Just make sure the environment is moist and not too hot or your seeds might be toasted. Is it winter in your country, young man?
See the colour on this towel?
Some seeds do bleed colour onto the medium!
You can see from the above pic, the roots will be weaving in and out of one another and you end up killing the seedlings when you tease them apart of when you grow them in masse, whichever way is not ideal.
You could trial this method
You could seal the whole tub with clingfilm or clear plastic to stop fungi growing in the soil or compost gnat laying eggs! Best is microwave the soil to sterilise it first and leave it to cool!
Bon courage, young man or young avatar!