Actually, masma, the subject of clematis pruning is rather straightforward. As you've already identified the flowering times of your plants the dtermination of the pruning (if any) is decidedly simple.
It seems you already have a clue since you do mention the flowering times.
Keeping in mind that all pruning is for the health of the plant in next years season, you'll find the Spring Bloomers produce their blooms on old wood... i.e., last years growth. Therefore you're seeking to eliminate this years new growth soon after blooming is finished. Avoid the larger, obviously old growth woody vines and cut off this years new, smaller vines. You can cut to your hearts desire or you may wish to just reshape the plant... regardless keep this goal in mind.
Summer and Fall Bloomers :
The goal here is to understand these bloom on this years new growth and really don't require much pruning with the exception of maintaining habit. Prune only those branches that are causing tangles or otherwise growing where unwanted. They should be pruned during dormancy... winter or early spring.
There is another varietal... the Repeat Bloomers... I have about 17 clematis and not one repeat bloomer so I don't have any advice on theses other than to say, they must be similar to the summer and fall bloomers and should only be pruned lightly unless you wish to affect one or the other of the blooming times. Prune in the spring and they will probably not produce much of a spring bloom but do well later int he summer... prune after the spring bloom and you won't expect much in the fall...
Best of luck!