In practice, you build up a really big combined future on the stack, which has all of the space needed for any state in its state machine, and then when the future is fired off (in a task -- one per connection), that entire thing is moved into the heap in one shot. Thus, generally, you do one big allocation up front per connection -- exactly the same as you'd do when writing state machines by hand.
The follow up posts will go into much more detail on this point :)