No, just keep doing what you're doing after you double check a few things. Some household TP will not break up in water but now many brands will. Put a sheet or two in some water in a glass jar and shake only once or twice. If the TP completely blows apart, you're good to go. If not, find a brand that does. I use a clear elbow at my dump outlet and it allows me to observe that there are no chunks of TP.
Lots of water prior to dumping is the key. I tend not to use my black tank flush but most people, I think, do. So far no problems. Others will chime in on the things that I've forgotten.
No need to use RV toilet paper unless your TP fails the jar test.