Were they in full sun where you found them? I'm sure they're in shock right now, so moving them to partial shade with only morning sun would likely help out a little. Don't over-water. In fact, resist the urge to intervene for their own good. Passis are a robust species. Even if the vines die, the roots will most likely send up new growth in a couple of weeks.

When I take suckers with roots or dig up transplants I always pot up with lots of coarse sand and/or perlite mixed into the dirt mix. The reason for perlite/ or coarse sand is that these plants have lost part of thier root system. Usually the fine hair roots at the end of the roots which get torn off, are damaged when you dig them up. So since they cannot take up as much water as when they were growing before they were dug up, they will need excellent drainage until they grow back. Don't worry about flowers until your vine is healthy. Plants will often sacrifice flowers until thier roots and then leaves are healthy. You could even cut the vines back shorter so the roots don't have to support so many leaves. They should grow back quickly once they are out of shock.
Water them with water and a few drops of superthrive or vit B mixed in. No plant fertilizer, because these plants are in shock and fertilizer at this point could kill them. Keep them in the shade until you see that they are putting out new growth.
You may be able to water root some cuttings as well. Take about 6 inches of new growth from the tips of healthy vines and take off most of the large leaves and just leave a few small ones at the growing tip. Place them in a window that gets filtered sunlight and make sure the water stays clean. I use clear glass jars which seem to work the best. It takes some time but they usually root.
~SJN

Cutting the plants back by half is a good idea. They'll grow quickly once they recover, so the lost vegetation isn't much of a loss, and will probably speed recovery.

You can try rooting the cuttings in water, or use a rooting hormone and put them in a wet sphagnum moss/pearlite mix inside a plastic baggie in a sunny window. Don't hold your breath, though. Incarnata has the reputation of being one of the most reluctant passis to root from cuttings. I tried a lot last year, and out of nearly two dozen attempts, only one took. :-(

Just keep them in a shady spot with evenly moist, not wet, soil and NO fertilizer. New transplants shouldn't be fed right away. Just use ST and B1, like SJN said. As long as the fertilizer didn't kill the roots the vines will probably put out new growth in a couple weeks. Once that happens slowly give the plant more sun and allow it to dry more between waterings. Try to reproduce the conditions that it was originally growing in. Good luck.
Karyn