A month huh? Hmmmmmmmm.
That would be one nasty carbon filter in a month, a real nitrate mess.
I have seen crazy instructions leading to timelines like that on products but honestly its a on basis need far as cleaning & replacing goes & ea sys is vastly different.
I don't run carbon usually just no need in a mature tank with few nasty toxin producing softies except maybe my Ricordea shrooms but i have some ready for use if i was in need due to some emergency that might arise.
And when i was using it in the early days id inspect it every couple days & wash the filter pac and the carbon in old tank water to clean off gunk then re-use the carbon again for a max of 2 weeks, seemed to polish the water nicely but again yea even the carbon gets muck buildup on it if just left as a long term bio filter and needs to be cleaned periodicly if its to keep being used as expected with results, otherwise just rinse the dust from new carbon & replace if easier & not an expense or on hand issue.
Anyway, this is what worked for me when i had a lot of softies before i went to hard coral and i never had Zoos or Palys due to toxins but carbon would be a good 24/7 on a DT over flowing with that type of stock.