I did the same as you a couple years ago. I checked my ticket and had no assigned seat.
What happens, from my memories, is that it will basically be a first-come, first-served assignment of seats. There is no big crowd or anything, just everyone gets on board pretty much at the same time and picks a seat. On my train, every traveller or couple had his own double-seat and it was in July, so there is no need to rush. It is still important to pick a good seat because once everyone is sitting, the train agent will add a marker above your seat to "reserve" your seat.
A seat may be good because it has a large window to enjoy the view, it may be bad because it is too close to the bathroom (bathroom is clean, but there might be many people passing by) or to the car entrance.
Even if you have your own double-seat, you might still have a neighbor getting on at a later station. And if you end up with a "bad" seat, you will anyway be able to spend much time in the dome section of the skyline car.