What is the moment when all oscillators aligned to make a jump called?
I think the word/phrase you are looking for is "discontinuity" / "discontinuity in the source signal".  Although a jump is always a discontinuity, a discontinuity is not always a jump.  When it isn't a jump, it is known as a pluggable discontinuity, i.e. you can define a value to plug a hole.  The sinc function at zero is an example of this.  So to be more specific you would say "an unpluggable discontinuity".

Whether a series of continuous functions could converge to a discontinuous function was a question that led to some very serious, and non-intuitive, math.

As far as I know, there is no word to describe the state of the components at this moment.  The closest word I can think of is a secondary meaning of "concordance" = "agreement".

Hope this helps.

Ced