There is indeed specific moments when you get palace upgrades. I compiled a list a while back but it got thrown away during a spring clean, as most of my game related scrawling do.
As you note, the first one always occurs with the founding of the 2nd city. I noted several others, including hitting some round numbers in culture score but most I have forgotten
It is also true that sometimes I could see no specific event which generated it, but later on in the game so much can happen in one turn that it's to time consuming to investigate every little event - particularly in a turn where every stat changes and the entire world is at war.
That these specific points don't occur for some people sometimes is likely the minority rather than the norm and this feature is glitched as in some games you can go centuries without any then it'll give you three at once as if it's on some kind of delay, or, as Rodrig0 states, they are there but it just doesn't notify you for some reason.
The civilopedia is a wonderful tool, but I'm regularly amazed by what information it DOESN'T contain, such as a palace description page, any definitions of town, city and metropolis (you have to guess from experience) and the exact matrix for war weariness to name but a few.
On the one hand the game makes you believe you can plan for everything with the correct micro-management while on the other it seems determined to keep so much a big secret that complete micro-management still doesn't really help as much towards a grand plan as you might think.
The developers must have instigated a matrix for every little detail, so why can't they have an explanation page for every little matrix they implement. For example, we know Infantry has a defence of 10 and can still be killed regularly by an attack of 4 - what we're not told is what the roll is based on - if it's a 50 sided dice the 4 versus 10 is not that much, if it's a 10 sided dice it's a whopping difference for example.
I think it would have been relatively easy for the palace screen to have a simple dialogue box which states 'Because you did this/that/the other the people have expanded your palace'. And equally simple to have a civ page which lists all the triggers.
Unless it's not quite that simple of course - but then why not a page explaining why it's not that simple or an indication of how random it is if it is random (which I don't believe it is).
Soundbite: Rodrig0, I recommend you experiment with culture score, both whole civ and individual cities (particularly capitol) on round numbers such as 10, 100, 1000, 2000, 10,000 etc.
As you note, the first one always occurs with the founding of the 2nd city. I noted several others, including hitting some round numbers in culture score but most I have forgotten

It is also true that sometimes I could see no specific event which generated it, but later on in the game so much can happen in one turn that it's to time consuming to investigate every little event - particularly in a turn where every stat changes and the entire world is at war.
That these specific points don't occur for some people sometimes is likely the minority rather than the norm and this feature is glitched as in some games you can go centuries without any then it'll give you three at once as if it's on some kind of delay, or, as Rodrig0 states, they are there but it just doesn't notify you for some reason.
The civilopedia is a wonderful tool, but I'm regularly amazed by what information it DOESN'T contain, such as a palace description page, any definitions of town, city and metropolis (you have to guess from experience) and the exact matrix for war weariness to name but a few.
On the one hand the game makes you believe you can plan for everything with the correct micro-management while on the other it seems determined to keep so much a big secret that complete micro-management still doesn't really help as much towards a grand plan as you might think.
The developers must have instigated a matrix for every little detail, so why can't they have an explanation page for every little matrix they implement. For example, we know Infantry has a defence of 10 and can still be killed regularly by an attack of 4 - what we're not told is what the roll is based on - if it's a 50 sided dice the 4 versus 10 is not that much, if it's a 10 sided dice it's a whopping difference for example.
I think it would have been relatively easy for the palace screen to have a simple dialogue box which states 'Because you did this/that/the other the people have expanded your palace'. And equally simple to have a civ page which lists all the triggers.
Unless it's not quite that simple of course - but then why not a page explaining why it's not that simple or an indication of how random it is if it is random (which I don't believe it is).
Soundbite: Rodrig0, I recommend you experiment with culture score, both whole civ and individual cities (particularly capitol) on round numbers such as 10, 100, 1000, 2000, 10,000 etc.