Divergent sequence of clock genes in different organisms are not a barrier for a convergent evolutionary clock.
How circadian clocks were evolved is a big topic. At the first sight, it might be hard to believe that the clock we have seen in fungus, animals and many other organisms share similar mechanism. Well, it was also hard to believe that the complex behavior like rest/activity is regulated by only a set of clock genes. After all, bacteria, plants, insects and us have a common ancestry.
This is a nice essay from Drs. Loros and Dunlap regarding the origin of circadian clock in Eukaryotic cells.
http://www.cell.com/molecular-cell/abstract/S1097-2765(17)30887-0