Control when Reminders show in Notification Center
You can set a specific time for a reminder: mouse over the entry in Reminders and a circled "i" for "Information" will appear, upon which you should click.  Then select the checkmark box, "Remind me: On a Day," and fill in the date and time for the reminder.  

The Reminders functionality in OSX and iOS is minimal; Apple seems to have wanted to include a product to be able to say they did, but not one that actually competes with any of the third-party vendors, to avoid strangling the software ecosystem like Microsoft did with Outlook.  You might look at a third-party software package to meet your needs better.