I would hold off fertilizing any budding up clematis right now with 10-10-10 as it tends to dump all of its nutrients as it gets wet and that could affect your bloom cycle. I fertilize with organic slow release fertilizers typically in the early spring as the plants emerge and then later in the season after I cut them back. I have even fertilized when plants were blooming with organic slow release fertilizers and not had any effect on blooming. What you don't want to do is hit the plants with immediate release high nitrogen fertilizers as those are the types that have been reported to cause a shortening of your bloom cycles.

As for cutting back after blooming, it depends on why you are doing it. If you want to try and get a second bloom flush out of the plants, then cutting back either type II or IIIs by half or more, giving them fertilizer and water, and seeing if you can get a second bloom flush is no issue. If you are cutting back to contain the plants' size, then after blooming is generally the best time for type IIs or early in the spring for type IIIs.

I am not really trying to contain any plant size yet. I just thought it might be healthy for a plant like this one:

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It is an unknown type 3, litle growth last year due to a drainage problem. All of that growth is off of 2 main stems. So it is a little top heavy. Not knowing the cultivar, I selected a 6 foot trellis and it started to outgrow the top so I just wrapped it around. Could this benefit from cutting down by half after bloom? Would that possibly produce another stem?