Can private servers get our credentials?

I never played in any pservers because of two reasons: lag and bugs. I can max 8/8s constantly in prod so I never had any reason to join those.

However, I did register in a pserver months ago, don't remember the name of it, was lagged as hell and there was duping.
When I opened the pserver's swf, my prod credentials were in the menu screen and it seemed like if I was already logged in, with my email(you only needed to register with a nickname) and the client probably got the password from the .sol file too. I left the server and changed my password after that, but I still don't know: can the pserver owners get the information from your .sols with a swf?

Yes. Always log out of your prod client before opening a private server client. When you load the client, you send a request to the server (which in private servers is changed to their own server) with the last used account details. If the private server operator logs char/list requests they can see any accidental prod logins.

When you are logged into any client, going right to another client, even if its not the current Fabiano (closest to prod source) source, it will show you logged in as your last client logged in account and it most likely will show some kind of message in the server.exe log including the credentials it attempted to log in with, yes it has to do with the .sol files, just simply log out of prod client before opening a pserver client, also don't register with your username/password even if you didn't accidentally get the glitched prod login on a pserver client, because it is extremely easy to remove the SHA1 encryption from the passwords, to where your password shows as regular characters in the database, just use a fake email, no pserver owners even use the forgot password feature or anything involving emails.

I have a mule with 8 life on it that i have logged in when I try pservers for approval. If they go missing, I then know where to look.