I had to replace both solenoids little over a yr ago .Same asa you , turnig off the key didnt stop the motor. I had to remove the battery lead .It happend again the other day but I found this time the starting push button was sticking now .In this case it did stop with turning the key off.IT seemed to happen after a ride in some rain .
Yep, 100% you have a solenoid with fried contacts. I have repaired a couple, but the springy metal that opens and closes the contacts get hot and annealed. This makes the springy-ness go away, and the re-burnishing the contacts won't last. This condition can toast a starter, so it's not worth trying to fix. Get a new solenoid. JMO jimsjinx
I just had the same problem. In my case, though solenoid "A" tested good, replacing it fixed my problem. Solenoid A is the one up next to the battery.
In my case, the starter kept cranking with the kill switch off but the key switch on. Turning the key would stop it, then switching it on would immediately start spinning the starter, before touching the button.