Synchronous vs Asynchronous Counters for Periodic Phenomena
It is best to use the second counter with a synchronous design and share the same clock between both counters. 

Use the decoded "decade pulse" as a count enable of the second counter.

Use the decoded "decade pulse" as a synchronous load back to zero of the first counter as opposed to connecting it to an asynchronous clear input. 

The reason these steps are very important is because it is possible that the output of the decade decode AND gate output could have glitches on its output as the counter outputs change state. Using that output as a clock could result in the glitches giving extra clock pulses.