Hi Amer
I have the same Autavia GMT as you. It is NOS with serial number 1312xx. I can confirm that my example has smooth pushers and a large crown (approximately 6.5mm diameter & 3.5mm deep). In the picture below there are reflections on the pushers but I assure you that these are smooth and NOT fluted. However, in Arno's book page 39 his example which has the same dial and hands as ours, has fluted pushers. If you look at the pictures of this reference on the OTD site both style pushers are found on these examples. I would therefore assume that this reference would be correct with either smooth or fluted pushers. Maybe the early examples had smooth pushers.
regards
Paul