The phrase "actually after the first" is correct and usable in written English.
It can be used to clarify a sequence or timing in relation to an event or item that follows the first in a series.
Example: "The meeting will take place on the second Tuesday of the month, actually after the first."
Alternatives: "specifically after the first" or "in fact after the first".
Actually, after the first few years of his presidency he played golf for a few hours on many weekday mornings, returning to the White House around 11 a.m.
It is not clear how influential Demosthenes' advice was—or how influential, at this stage, it deserved to be: at about the same time, and, perhaps actually after the "First Philippic," Demosthenes was found advocating, in the "Speech on the Freedom of the Rhodians," a foolish diversion of resources to the southeastern Aegean against the encroachments of Mausolus's family.
I didn't pick the title, but, you know, we changed the title actually, after the first visit.
And actually, after watching the first part of this (possibly) very entertaining untangling of the double agent's career, I'm wondering if I even know him a little.
"We were actually down after the first day so we weren't completely convinced it was going to happen," junior Caitlin Morrissey said.
Perhaps the worst-case scenario, though, is when the inmates don't actually die after the first few minutes in the electric chair.
In terms of costs or resource usage this would be, on the contrary, a more liberal way to proceed in the event that a truly new injury had actually occurred after the first admission.
But actually, after the (thrilling) first time, it's just because I'm old, don't really feel like leaving the house, and anyway am too infirm to do so.
But actually, after that first climax of delight in being able to bang in the final bit of the historical jigsaw, a curious flatness sets in.
When things are going very well he sometimes gets a bit impatient as to why they are not going better, but he was actually very calm after the first debate," he recalled.
But what should have been a nicely observed piece of satire actually fell flat after the first couple of slides.
