According to the Forham sourcebook site
https://sourcebooks.fordham.edu/basis/v ... antine.asp
which uses
Volume I, Nicene and Post-Nicene Fathers, 2nd Series, ed. P. Schaff and H. Wace, (Edinburgh: repr. Grand Rapids MI: Wm. B. Eerdmans, 1955) yhe digital version is by The Electronic Bible Society, P.O. Box 701356, Dallas, TX 75370, 214-407-WORD.
Book 3, chapter 67 seems to refer to a specific kind of reverence shown to Constantine's corpse by his courtiers while he lay in state (so to speak). After chapter 66's setting the scene of a gold coffin with porphyry ornament set on a catafalque, chapter 67 describes this curious solemnity (quoted here in its entirety, but paragraphed for readability and ease of reconciliation with the OP):
THE military officers, too, of the highest rank, the counts, and the whole order of magistrates, who had been accustomed to do obeisance to their emperor before, continued to fulfill this duty without any change, even after his death entering the chamber at the appointed times, and saluting their coffined sovereign with bended knee, as though he were still alive. After them the senators appeared, and all who had been distinguished by any honorable office, and rendered the same homage. These were followed by multitudes of every rank, who came with their wives and children to witness the spectacle. These honors continued to be rendered for a considerable time, the soldiers having resolved thus to guard the body until his sons should arrive, and take on themselves the conduct of their father's funeral.
No mortal had ever, like this blessed prince, continued to reign even after death, and to receive the same homage as during his life: he only, of all who have ever lived, obtained this reward from God: a suitable reward, since he alone of all sovereigns had in all his actions honored the Supreme God and his Christ, and God himself accordingly was pleased that even his mortal remains should still retain imperial authority among men; thus indicating to all who were not utterly devoid of understanding the immortal and endless empire which his soul was destined to enjoy. This was the course of events here.
It would appear, then, that
to continue to reign even after death is neither a reference to the historical Jesus nor to the practice of deification. Rather, its referent is Constantine's surviving courtiers behaving around his corpse much as they had behaved when serving the living ruler. That is, another way of expressing
to receive the same homage as during his life after he'd died and before the final disposition of his remains.
Or so it seems to this reader.