Why don't you write "IMMEDIATELY after"?
Why not? Because the point was the second coming which was "after" the Holocaust. What came immediately after was first the interval of darkness of the sun and moon and the stars. This is considered to be a spiritual darkness among the anointed with respect to the details of the second coming. This is the "nodding" of the ten virgins just before the second coming, showing that they would be sleepy as far as their full understanding of the date and nature of the second coming.
Daniel, of course, times this interval of darkness occurring "immediately" after the great tribulation as being at least 45 years after the "end" of the 1290 days which would be near the end of the "great tribulation". The great tribulation was to be the final last blow against the Jews for leaving God's covenant, after which his anger would be "rested" and he would then forgive the remnant of the Jews and restore them as his people and reestablish them in their homeland as promised, which occurred in 1947.
So, if you wish, as far as detail goes, what happens "immediately after" is this darkening. The second coming is 45 plus years away at this point, so thus no need to emphasize "immediately" in regard to the second coming, only "after". I wasn't trying to avoid the "immediate" reference.
Some have focussed on this since they'd presume this was a second coming reference and thus would suggest that the second coming came immediately after the HOLOCAUST, but that is not specific to the text, just in case you were going in that direction and entertained that argument before.