No,
Inside each tube there are two pouches of bluing.
One dips the pouch of bluing into water again and again until the proper amount is dispensed. Then the bag is carefully "wiped" and set upon a vented surface to dry. Once dry it is put away until next use.
Bleachette is simply a packaged/ready made version of "dolly blue" bags long used on both sides of the pond. In olden days housewives, laundresses, or whomever was doing the wash purchased either powdered bluing in bulk or cubes, and wrapped the stuff in bits of flannel, cheesecloth, or old linen (my favourite), and used as above.
Find the paper "cloth" used to wrap Bleachettte can tear over time with use, so I rewrap in a bit of old linen from my sewing basket.