....If President of Hyperion and CEO aren't the same thing....
And Jack's words in TPS are "If I ever become CEO" ,
Not "ever in charge"...
And not 'President' - how he introduces himself in 2...
...Then how did I not consider he might already be president in TPS, just not CEO.

President would have all of the oversights he already had and would need to have that much influence and control over the station, and to have Angel's set up (something he had in BL1). And being /just/ a programmer is the lie, he is still /a/ Hyperion programmer, which tracks.

Jack's not necessarily an out-and-out liar - he's manipulative and deceitful, but his preferred tactic is 'lying through omission'. And it's enough of an omission that makes it weird that 'just a programmer' needs a body-double so bad.
But it's /not/ so weird for a President.

Especially not one for a major weapons manufacturer that's trying to open a Vault, under the guise of everyman-but-still-badass Vault Hunters. Which was Jack's bit in 1 - he had Angel and the VH's do it. And he was doing something of the same in TPS.

And "Jack doesn't pay me enough" being as complaint, things already being Hyperion yellow even when the official brand is red, Jack having the /ability/ to construct an entire station and being able to do so under his direction...

Yeah...
Jack's already President in TPS.

So, it's still Tassiters office - but it... might be Tassiters office when he's /there/.
It could very well be /also/ Jack's office.