It depends..
If you're running the lovense overlay, and it pops up there, they will be able to see that of course! if it plays any sounds, they will be able to see that also, It's a long time since I have used CB for privates, but when I did (last summer) I remember one guy would always tip in the public room for a girl, and they sound would still go off in the private..
however it will not pop up in his private chat window at all who tips and how much etc.. if the tips are in the public chat, he won't even see it unless he also have your public chat open somewhere..
if you run the lovense Overlay, a way to get around it is to remove the overlay for privates if people do not have control there, and it's also possible to mute the tip sound if that is what bothers people.. it's a weird thing to get bothered by, but hey, I know some do, and some guys also tip while specific guys take a girl private (I got told by a model that someone only tipped publicly whenever he found out it was me taking her private for some reason)
I hope this can somewhat help