This term stems from the word "cascade" as deriving its sense originally in the technologies of electronics.
It is found in electronics in connection with amplifiers and digital cicuits; when you say that amplifiers are connected in (a) cascade you mean that the output of an amplifier is connected to the output of another, that is, in other words, that the output of an amplifier feeds the input of another. One speaks often of a cascade of amplifiers. The idea is similar for logic gates. It communicates roughly the notion of "one after the other".
The same idea is found in chemistry.
(Wiktionary) (chemistry) A series of reactions in which the product of one becomes a reactant in the next
The word "cascadingly" has since then been used in various fields with this meaning : electronics, mathematics, physics, artificial intelligence, neuroscience, philosophy of technology, sociology, … (cascadingly)
This term has been found in the fields just mentioned and many other connected fields since the beginning of the 21rst century; it has come to be used even more widely to "overspill" into the humanities and current language.
(Wiktionary) cascadingly (comparative more cascadingly, superlative most cascadingly) In a cascade; as if falling one after the other.
Apparently, this is a term that has gained a wide enough currency, indisputably so in specialized fields and also in the current language, although in this latter domain usage might still be shaky.
If you want to rephrase this you have to understand that the use of "cascadingly" presupposes the existence of elements that are somehow connected, and rephrasing should include mentioning them. If, for instance, the job consists of a number of separate calculations that give rise to accessory manipulations of no further use after the results are obtained, then these calculations have to be mentioned (by whatever name they go by usually).
- When the TTL controller cleans up the Job, it will delete the sets of auxiliary computations one after the other.
There is a term that is very similar to "cascadingly" because the steps do not have to be recalled; it is the term "sequentially"; however, it does not express the idea of one process triggering the next as markedly as "cascadingly".
- When the TTL controller cleans up the Job, it will delete the Job sequentially.