I've seen the waiter's tray position (first)
manifested at different phases of the service motion for different servers. Some players will exhibit the waiter's tray at the "trophy" phase of their motion; while others will have something resembling a somewhat conventional trophy phase/position, but then improperly drop the racket to a waiter's tray position. Both of these will often be a result of a lack of proper supination of the forearm. An improper extension of the wrist (or an improperly timed wrist c0ck) can also be part of the problem.
A third possibility for a waiter's tray error can happen some time after the racket head drop. In some cases, the forearm may have been supinated earlier in the motion but then is pronated too early resulting in a waiter's tray at the "big L" phase (where the arm has become full extended but the racket is still more-or-less parallel to the ground). There are also some players who exhibit a waiter's tray but never get to the "big L" because they never straighten then arm on the upward swing. Other aberrant serve motions (in addition to the ones I've mentioned here) may also result in a waiter's tray error.