The adder is not clocked. You can see from the diagrams that there are no clock inputs. The clock cycles comment is more an expression of the length of time that it takes before all of the carry rippling and whatnot settles down.

In more detail, the microcode engine normally executes one micro-instruction per cycle. For addition, the engine is blocked for one extra cycle to give the result time to percolate through the adder.

There is some complicated timing within a clock cycle with slightly delayed clocks and whatnot, for instance, to precharge the carry lines at the beginning of the operation. The 8087 is mostly synchronous with the clock, but they "cheat" in many places.