In my experience, FIP 1st class coupons are fine in the 'Business Class' = normal 1st (2+1 seating) but not in 'Premium class' (1+1 seating in compartments). The ATOC guide is ambiguously drafted, but I think that what they mean is 1st = Business, 2nd = Economy and no FIP at all in Premium. However, in Austria you will find the odd conductor that insists a charging a supplement for the use of the FIP coupon (of about EUR3 per journey). Having checked this over and over again with OEBB staff at stations, this is not the case. But a number of conductors have I met have been quite insistent that this is the rule: I expect this is something from the past that has now been dropped but not all staff have clocked it.
The other thing about Railjet services in Premium class is that they have friendly at-seat service of food and drink: one has to pay but it's very good value (a bit like GNER was once upon a time). This is really the only railway in Europe left doing this in my experience!