A cycled (established) tank is one whose filter bacteria can neutralise ammonia and nitrite to zero, and a mature tank is one that has run stably long enough to develop biofilm and stable chemistry.
Sensitive fish and algae-grazers like otocinclus should only go into a mature tank, because a brand-new cycled tank has not yet grown the biofilm and micro-life they rely on.
"Give it time" is real advice: many problems in a young tank simply settle as it matures over the first few months.