Yep I think the above seems pretty legit. When you advance round, you make all the changes at the end, and they depend on the stats at the beginning. Round 0 begins with everyone having nothing, just getting 5 resources to settle, there's no technology being given as income. So no tech at the end of round 0.
People may have set high tech rates during round 0 so that in round 1, a part of their income is spent on tech. Which would give them the tech when round 1 ends and 2 begins, but still starting round 1 with 0 tech.
I recommend updating the scoreboard when a round ends, to be on the safe side so people don't go into it and use the stats on there for their turns. And when advancing the rounds, it's useful to copy the spent on tech and income values to the 2 small columns under notes (I've just done that). This way you can change the values for the different players without affecting the values you need to use for the other players later, when advancing the round.
(E.g. you update Kalassak's production to 9001, now suddenly the cells at Darvince says he gets 69 income from trade, and you make the error of including that when doing his turn - that's an important error to avoid)