Split streaming is so common that I stopped caring long ago about who else could see any privates I initiate, in the same way I cannot stop anyone from paying to spy either.
At least spying increases the model's income, and extending that, keeping other sites live gives the chance to earn more tokens and not lose the audience.
I would never assume you are truly private, unless you are paying for a premium exclusive arrangement, or have agreed up front that the model will turn off all other sites and turn off spy mode.
As long as whatever anyone else tips for doesn't really impact on my enjoyment of the private, I don't care. Things like mentioning another tipper by name, responding to DMs etc would be very off-putting.
Otherwise, I'd rather the model maximised earnings, their time is valuable and most token site private rates are still very fair, so this helps.
Just be aware that if you do c2c with audio, anything you say could be heard by others, and your voice may be very recognisable!
ETA: the only downside of broadcasting private action (from my perspective) is that some viewers just don't understand what they're seeing is being paid for and directed by someone on another site, and this can lead to an expectation that they get 'free' shows, or that a couple of single tokens get great results! And of course, it encourages the freeloaders to hang around and expect a good show for nothing.