Arduino - Trigger an iPhone's touch screen with no human interaction
The critical point here is to control the ground of the phone. 

When you manipulate your phone for its normal usage, one hand is touching it and sets the ground. Trying to do the same manipulation with a phone sitting on a table will be less reliable.

To have the same effect in the lab, you should have your phone laying on a conductive layer that is connected to the ground (or any other fixed potential) of your circuit. A simple way to do so is to have your phone laying on a copper foil that is used as the common ground of your circuit.

Your phone does not need to have direct ohmic link to ground, a good capacitive coupling is ok too.