If you are using Yahoo with Outlook you probably have a Plus account (I could be wrong, someone else reported being able to get Yahoo mail in Outlook without a Plus account).
Yahoo's server is a POP3 server. This normally removes emails from the server when they are downloaded, but it can be set to leave the emails on the server. That seems to be what is happening. You can double check that by going to the web client and seeing if the emails are still there.
The iPad account however seems to be IMAP, or at least it does a few things that POP3 accounts can't normally do. I have no idea how Apple swung that trick, probably with some sort of agreement with Yahoo.
IMAP accounts reflect what is on the server, so if you are seeing emails on the iPad it is because they were never deleted from the server. Outlook left them there, regardless of what it looks like on the computer.
At any rate, if you delete emails on the web client they will remove themselves from the iPad when it checks in (if not immediately then after tapping the Update icon). That also suggests the problem is with how Outlook is getting and dealing with emails, not the iPad.
If you go through your POP settings on the yahoo email site (only available if you do have Plus account), you could find a way to change this. You may want to go through the settings in Outlook as well. However, if you do get Outlook to start deleting the emails, hold in mind that you will not be able to see them on the iPad anymore. They will probably also be removed from the server all together, since Outlook will probably move them to it's local Trash folder rather than the one on the server.
Since I don't have Outlook to play with I can't confirm some of what I said, which reduces that side of things to speculation. Still, I hope I've given you enough to at least poke around a bit and figure it out for yourself.
