A good number of the pruning type 2's or the large flowered hybrid clematis bloom on both last season's growth and to a lesser extent on current season's growth. So yes, a spring flush and a lighter late summer/early fall bloom is pretty common. Pretty much all the double flowered clematis fit into this category, producing a lot of double flowers with the spring bloom and fewer, typically non-double flowers with the later bloom.

To maximize flowering, type 2 clematis should be pruned lightly (removing about 12-18" from the top of the vine) in late winter and agin lightly after the initial bloom flush.

Thanks Gardengal :)