If you mean the tank when you say cylinder then the tank needs washing in plain water after you empty out the fix but this will happen anyway when you remove the remains of the fixer from the film by filling with the tank with water, then agitating the tank several times and then dumping the water.
I assume that after emptying the fix that you wash the film on the reel in the tank? I use the Ilford process which involves filling with water, agitating 5 times then dump. fill with water agitate 10 times then dump, filling with water agitate 20 times then dump. To be sure I have washed the film I actually do 15, 20, 25.
In case there is any chemical now stuck to the reel use a toothbrush with warm water and scrub the reel. If you now follow the full process of develop. stop, fix and wash there should not be any need to use a toothbrush again
pentaxuser