PTZ cameras can be controlled by assigning a PTZ shortcut to an input where PTZ has been configured.
For example the shortcut "PTZMoveUp" once activated will keep the camera moving upward until a corresponding "PTZMoveStop" shortcut is activated.
For more information on the shortcuts available see Shortcut Function Reference
vMix includes a shortcut template that assigns PTZ control to joysticks and buttons on a USB XBOX controller
By default this template assigns all the buttons to the Preview input which means as long as a PTZ enabled camera is in input it can be moved and controlled using this template.
Of course, the shortcuts in this template can be edited to assign to a particular input if you prefer.
By default, PTZ shortcuts will use the speeds defined by the sliders in the Input Settings PTZ tab.
To specify a custom speed, specify a fractional number between 0 and 1 as the Value of the shortcut.