When do you actually ask customers for a testimonial?

Most testimonial requests I've seen go out as an email, a few days or a week after someone signs up or buys. By then they're busy with other things, and a lot of those emails never get a reply.

So in testimonialsltd we added a second way to ask. You put a small prompt inside your own app or site, and you decide when it shows up. Like right after someone finishes onboarding, hits a milestone, or renews. It asks "How's it going so far?" with a star rating. If they pick 4 or 5 stars they go to your testimonial form. Below that, they get a private box asking what went wrong, and that only goes to you.

It also won't ask the same person again for 30 days, and it never asks someone who already left a testimonial.

I'm curious how other people do this. When do you ask for testimonials right now, and roughly how many people actually reply?

Also, sending low ratings to a private box instead of the form. Does that seem fair to you, or does it feel like hiding the bad ones?