I understand the intention to be that you spend the opponent’s turn evaluating your tech options. It is printed as the last step of a turn, because that is what you are supposed to spend your time on after passing the turn to your opponent. You don’t actually have to interact with your opponent, because the game is designed to be asynchronous. But you are expected to finish before your next turn starts, so the (somewhat arbitrary) idea is that it makes more sense printed as the last step of every turn, instead of the first step of every turn except your first turn.
In practice I end up watching my opponent instead of really thinking about techs because it informs my tech decision, and because they might make a rules mistake.
A technician when the draw pile is empty is a very different beast from a technician when the draw pile has cards, because you end up having to weigh the costs and benefits of causing the reshuffle before the tech cards are added to the pile, or allowing your opponent to keep whatever is in technician and reshuffle into the tech options.