The phrase 'immediately upon making' is correct and usable in written English.
You can use it when you want to emphasize that one thing happened right after another. For example, "The staff member resigned immediately upon making the announcement."
But immediately upon making the catch, Epps hurt his knee and fumbled.
A fascinating set piece in his memoirs describes Union soldiers putting up telegraph poles and wires immediately upon making camp.
"Almost immediately upon making contact, the adult males in the patrol party began attacking the unknown females, two of whom were carrying dependent infants," she said.
He attained the status of cult hero immediately upon making his U.S. début, in 2012, and he has spent the years since trying, with some success, to de-cult himself.
The Secretary shall pay to the guaranty agency any funds withheld in accordance with this paragraph immediately upon making the determination that the guaranty agency has made all such repayments.
Acute management of these patients in the emergency department involves several different steps, but most importantly, the diagnosis must be made quickly, and general surgeons should be involved immediately upon making the diagnosis of a perforated ulcer.
Serve immediately after making.
We are of opinion that while the circuit court has the power to do so, and may discharge the accused in advance of his trial if he is restrained of his liberty in violation of the national constitution, it is not bound in every case to exercise such a power immediately upon application being made for the writ.
Jean-Paul Sartre who quoted these verses in Black Orpheus, (1976, 43 44) immediately after made this remark: "Upon reading this poem, one cannot help but think of the famous distinction which Bergson established between intelligence and intuition" (1976, 44).
I have denounced statements he made immediately upon learning of them, as I do again today".
"But let me also be clear, Reverend Hagee was not and is not my pastor or spiritual advisor, and I did not attend his church for twenty years". He added: "I have denounced statements he made immediately upon learning of them, as I do again today". At a campaign rally in February, McCain said he was "pleased to have the endorsement" of Hagee.
