When I have used insecticidal soap in the past, I also noticed the plants didn't really like it. But, it was in the Winter (plants were indoors) and I didn't rinse the soap off. After that, I started rinsing them off after an hour or so and they seemed to take it a lot better. Since yours are outside, I could see the same situation happening more quickly.

First off, I would expect your plants will be fine. I would just apply in shade / weak sun as you did before, and rinse them shortly after application. Repeat as necessary every 2-3 days. Since the soap is a contact thing, it doesn't take long to work it's magic on the aphids.

What tsheets' said about rinsing them shortly after application and repeating as necessary every 2-3 days.

Soak the plants like you did and then wash / hose them off after 20 minutes.

Some commercial mixes have horticultural oils in them or use salt "soaps" for their sprays.

I prefer to mix my own water/soap mix, skipping the extras that helps the spray stick to leaves. The initial contact does almost all the job and it doesn't need to hang around forever. I live in a decently humid environment, though...it might be a different story in a dry climate. Either way, I'd mix my own based on cost...and any sprayer you pick for it can be re-used because it's just soap water you're putting in it anyway.

nc-cm: That is what I am going to do. I have an Ortho brand of insecticidal soap now, but when it runs out, I am just going to grab a bar of my wife's home made soap. She makes it on the stove with oils and LYE of all things just like they did 80 years ago. I have a feeling it will work as good or better than store bought stuff.
Bruce