Is there a specific rule for a counter to go through states?
The book is correct. See it in this way as soon as connections are made, and clock pulse hits the ckt. is established there would be a signal 1 to OR2 which will turn the value of Q2 will be 1 as toggle is one. 
Thus output changes from 00 to 01

On second pulse or2 remains 1 and or1 also becomes 1 thus tff1 is 1 thus output becomes Qff1 becomes 1 . Here imp. point is Tff2 is still 1 changing Qff2 to 0.
Output changes from 01 to 10.

In third cycle or1 still gives out 1 thus togggle is on and Tff1 changes to zero. As Qff1 is thus rendered 0 no toggle in Qff2 occurs.
Output changes from 10 to 00.

So on the cycle continues.