That's my understanding too. The sales literature might be a little misleading here as it shows all contemporary Carreras, Autavias and Camaros with smooth pushers, leading into the second generation Carrera models all with fluted pushers and it's quite evident that we see the latter two models with fluted pushers often in this period.

The chrono identification manual Jeff posted recently shows this quite nicely for the two-reg manual Carreras, one of only two occasions in that manual where a four-watch sequence is shown:

Each of the first generation watches is shown with smooth pushers, with the second generation watch having the characteristic fluted ones. And we see the same from samples in the wild - first gen Carreras, even late ones like 30s, overwhelmingly come with smooth pushers. I always take anecdotal evidence with a pinch of salt - is the first owner enough of a watch savant to remember whether a detail like the pushers were changed at service? It's not always the case, judging by what I receive in my inbox.