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I got a Sony Xperia Tipo last Christmas and I've always had this one problem with it. No standard headphones will fit into the phone properly. I can get it to work if I wiggle them properly but the slightest nudge to the phone makes the headphones stop playing. I've tried several sets of headphones with the same result. And no, I didn't get headphones with the phone
Sounds like there may be a problem with the phones headset connector. I recommend that you contact a service location or local Sony Xperia support (http://www.sonymobile.com/global-en/support/contact-us/) regarding this.