Specifically, the way the player who starts the next age is chosen is not correct. Here is the relevant passage in the rulebook:
The player who "begins the next age" is the player who goes first. If the players are tied on military, nobody gets to make a choice for the start of the next age. The player who took the last card must go first in the next age. On the website, however, the player who took the last card gets to choose who goes first. This is actually a substantial advantage.The player with the weakest military chooses which player begins the next Age. A player has a weaker military if the Conflict pawn is on their side of the board. In a situation where the pawn is in the middle of the board, the player who begins the next Age is the last active player (meaning whoever played the last card of the previous Age).