It depends on which type of e-mail you are using: POP, IMAP or Exchange. With a POP account, the e-mail is going to go to each device unless you delete it from the server. Yes, you can set it up to delete the mail from the server so it won't stay in the trash, but I've never seen my POP account work fast enough so that it prevents it from sending to all my iDevices. I think, with a POP account, it sends the e-mail to all at once, so there is no stopping it. All you can do is manage 'after the fact" - use one of your devices to keep the server clean and delete on the server only.
I also use Gmail, which is an IMAP account on my device. In this case, the iPad (and all my devices) are seeing what is on the server and can intact with it. So, if I delete a Gmail e-mail from my iPhone, it will be gone from the iPad (and the web/my PC browser).
I can't talk about Exchange e-mail, as I don't use it. But, I think it works the same as IMAP.
Again, it depends on which type of account you have. Once you know that - you might be able to alter the behavior. So, can you ID which type you are using - then, hopefully, someone with the same kind will be able to tell you how to set it up (if you can).
Marilyn