Least you know what a Unicorn looks like 
I think the Ascension project was mostly a covert Cerberus project described in books, I don't know if they described a logo in detail. If they had one then it makes sense that Jack would know it, but I don't think we (the fans were actualy informed about it's looks) It's been a while since I read the book though.
http://forum.bioware...s-in-2160-2170/
I believe what the writers imply is that Cerberus was always the ones pushing human technological and political progression, but almost always behind the scenes. Originally part of the Alliance (though black ops), it became more and more independent until (mostly) splitting away from the Alliance in very recent years.
Pragia wouldn't have been directly rubber stamped by any particular Alliance officer, sure. But they also would have allowed Cerberus to do what it wanted in terms of biotic experiments, as long as the Alliance isn't blamed for it and has denyability.
So yeah, I'm pretty damn sure that Conatix was also, even if indirectly, an arm of Cerberus trying to encourage biotics in humanity.
BAaT was corporately created, with Alliance backing. It took the survivors of the eezo crash exposure (*cough* possibly done by Cerberus itself, to use for biotic experiments), and tried to forcibly train them.
Grissom Academy was Alliance run, but with clear corporate backing and civilian support.
Ascension Project was a specific project, that we *know* had Cerberus spies. But it was a more nuanced approach towards biotic experiments than both Pragia and BAaT.
My point here is that it doesn't matter what is claimed to be in charge of human-run program, when it comes to biotics. Cerberus had a role in it. Even if it was just a single scientist at times, pushing for more extreme training or research.
"Cerberus is humanity" seems like an automatically villainous statement, but if we logically look at how the story's been told since at least ME2 (but including ME1 material), then Cerberus pretty much *is* humanity. At least as it stands during the trilogy.
Shepard himself wouldn't have had his ships, his crews, his own life, his technology, a whole lot of things, if it wasn't for Cerberus. Even the Alliance since the First Contact War could have retreated into itself like the Batarians had done, but I believe it is implied that Cerberus influence kept the Alliance and Earth governments/religions/cultures from doing so, and instead pushing for interaction with the Citadel. Even as the Alliance declares Cerberus to be terrorists, they're still often allowed to be on their own business, Shepard is given leeway by an Alliance admiral (or two), and there is an atmosphere of sympathy about Cerberus in ME2. This only sours in ME3, when Cerberus takes more blatantly extreme acts and the wider public is able to compare them to the Reapers that they're fighting against.
Head vs Heart.