Omnitron-X has a card, Electro-Deployment Unit, that let's him play a card at the start of his turn. If he plays another Electro-Deployment Unit, will that also trigger, or will it be too late in the start of turn phase to still trigger this new card?
Yes, it will trigger, because it's still the Start of Turn.
Also any components played by an electro deployment will also do their thing.
Think of it the same as a villain or environment playing something during their Start/End phase which activates during the same Start/End phase, such as a Maintenance Level (Mars) playing another card from the environment, or Rat flipping (due to all heroes being Infected) and immediately dealing damage in his Start phase...or Dawn flipping and immediately flipping back if enough Citizens are in play to cause her to do so :).
Since cards which activate during phases like that activate in the order they were played (as opposed to stuff which is always active when in play, like Fortitude or Imbued Fire), if you use an EDU to play another component, that second component is therefore in play after the EDU which played it, thus will fit into the turn order being taken by all components currently in play - if there are no other components currently out, the newly-played one will activate immediately (as the EDU, in playing it, has now finished for the turn).