Sharunda, here's where to find the settings you seek. You have to set up this mailbox behavior on both OS X and your iDevice(s). I'm not sure what the factory settings are, so check your Mac(s) and your iDevice(s).
OS X
Launch Mail.app on OS X. Click on the "Preferences" menu item (the keyboard shortcut is "⌘,"). Click on the "Accounts" pane. Under the "Trash" heading, make sure "Move deleted messages to the Trash inbox" is checked. Do this for each account you have going. Screenshot:
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iOS
As for your iDevice(s), I could not find an equivalent "Move deleted messages to the Trash mailbox" setting on my iPhone. However, if you go Settings > Mail, Contacts, Calendars, then tap on one of your active accounts, you'll see some sliders. I assume that, if set to the "ON" position, anything and everything you do to your e-mails on the given account on your iDevice(s) should be synchronized all over. Again, do this for each account you have going. Screenshot:
View attachment 24302
Hope this helps!