I came up with the same result as you did when I did a simple-minded analysis on paper, but I ran a sim and got the same results as your sim did! The reason it does this is that, because of propagation delays, the preset ends at about the same time the last two stages get clocked. This allows both of them to toggle immediately after preset ends. You should be able to see this by probing the preset, Q, and clock inputs to each FF.
Try removing the inverters, and instead clock each of the last 3 stages off the Q* output from the previous stage. I think you'll get the results you expected (I did).
BTW, why did you use the inverters?