There is no way to touch toilet paper after someone else does without air contact even if you were together and tried to do it at the same time. I'm not sure what example you are trying to show because the tp down the toilet has nothing to do with the tp on the roll.
No worries, because you can't get hiv from personal contact except unprotected penetrating vaginal or anal, neither of which you did. Analysis of large numbers of infected people over the 40 years of hiv history has proven that people don't get hiv in the way you are worried is a risk.
To add on a little bit, air inactivates the virus. You will never get it from a surface. All transmission is inside the body.