Do you have the other side of the relay contact either directly or capacitively grounded to the phone body? Try laying the phone on a large piece of foil and use that as the "ground" side.
The touchscreen works by sensing current drain on an AC signal, when something with sufficiently large capacitance to draw power touches the screen.
The screen contacts need to be sticky or pressed firmly to the screen and then connected to phone "ground" to trigger inputs.
- Imagine you are holding the phone, you are emulating the path from a fingertip to the hand with the phone in it.