So so so yes. "It's exhausting having to keep going back to the previous turn to try to make a crucial move in hundredths of seconds before the AI cripples the move." I admit I do this alot when I forget to put automove on some units.

Theoretically they are on pause a little bit at the start of a turn. But it seems that pop-ups (new tech, ability to build a wonder) disrupt that and they move.

Note that this is controversial, some people say that making the AI wait gives you two turns in a row. Well, it's debatable because it's actually the AI getting two turns in a row (Turn1: you move, they attack and you retreat; Turn2: they move and attack, you die - that's two turns in a row for the AI)

If not mistaken a few patches ago we did some changes to avoid this feeling. 2 main things, if not mistaken if you pre-order X troop to attack Y from the enemy they will wait a bit more, in case you do the auto-action and same when claiming new territories if you pre-ordered to build an outpost you will have a priority (but I understand that there are other conditions in which player could be a bit stressed because of this)