Mostly withdrawal time depends on the cryptocurrency, you want to withdraw. Bitcoin for example can take several hours. ETH can take even several days.
Op is talking about processing is the time in which OP clicks on the email containing the withdraw link and has it in the history of withdrawal if the withdrawal has already been processed or not. if the withdrawal is processed it means that poloniex already sent the coins to your wallet and the person awaits the necessary confirmation.
Someone else having trouble with poloniex withdrawals. All my other withdrawals took only couple minutes to process. Today my request is pending already for 5 hours.
this is not a good sign