Generally I tend to feed clematis when in active growth, so early in the season. I have a fairly short growing season (5 months) and fairly good soil, so I add compost or alfalfa just once a year and they seem to do fine. I assume you have a longer growing season and if your soil is low in nutrients, you might want to feed midsummer as well, but I wouldn't feed in the fall, even though this is an evergreen, unless it is growing a lot at this time of year.

Hopefully someone with experience with this particular plant will have some advice for you.

You always want to feed plants when they are in, or about to enter, active growth. That typically coincides with springtime, whenever that may be in your location :-) That is when they are most able to metabolize and use the fertilizer. If you fertilize late in the season - your fall - it can stimulate the plant to put out new growth when it should be "shutting down" or entering a period of stasis or dormancy. Growth prompted in late season can be vulnerable to cold damage, should your winters actually get cold.