I'm sorry this is happening, but I think there isn't anything for it other than to pay a pro to come to your house and completely give everything a once over.
They should send a camera down the drain all the way to the street, and they should give you a copy of that captured video.
Otherwise, we are guessing:
- It could be an obstruction further down.
- It could be the fact that the washer drain, or a drain it connects to, is too narrow.
- It could be that this massive flush of water is trapping air somewhere when it fills the entire length of pipe, which would not be a problem with other tests that simply use less volume of water at a time.
The last one is often an issue with modern washers plumbed into a section of an older house without a real or adequate stack to the roof. As pumps got better, that minimal or bad stack arrangement was tested more and more to its limit.
A professional can help determine which one. As any plumber will tell you "there is always a reason for a backup". But those reasons are legion.
Also, a good pro will work with your regional liquid waste management folks to coordinate reports. Often your regional folks will want to hear about strange behaviour of equipment on their drains. I mean, there's the indemnity and responsibility parts of where in a drain the fault lies. But no one is interested in making sure you flood.