I think it applies to more than just your first puppet, but also for the first puppet you have after an annex.When you capture a city it's always counted as annexed before you pick the puppet option. Since the tech/policy cost only factors in your maximum number of non-puppeted cities, your first puppet will add to the costs.
If you continue puppeting only after the first, your tech/policy costs won’t keep increasing, but they’ll remain “off” by one, the first puppet. The first city you later annex shouldn’t increase your costs, but the next puppet or annexation after that should.