Your situation involves personal contact with an object in air ( tools, needles, blood from people's cuts, etc.). No hiv worries, because you can't get hiv from personal contact except unprotected penetrating vaginal or anal, neither of which you did and you didn't share hollow needles to inject with which is the only other way to acquire hiv. 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.
HIV is a fragile virus in air or saliva and is effectively instantly dead in either air or saliva so the worst that could happen is dead virus rubbed you, and obviously anything which is dead cannot live again so you are good. Blood and cuts would not be relevant in your situation since the hiv has become effectively dead, so you don't have to worry about them to be sure that you are safe.
There is no reason for a person to test when they are safe. The advice took into consideration that the other person might be positive, so move on and enjoy life instead of thinking about this non-event. hiv prevention is straightforward since there are only 3 ways you can become infected, so next time you wonder if you had a risk, ask yourself this QUESTION. "Did I do any of the 3?" Then after you say "No, I didn't" you will know that it's time to move on back to your happy life.
Your situation of being cut and rubbing someone else's blood and cuts is common to everyone on this planet, although maybe it doesn't happen to others as much as it does to people in your profession, but you have never read of anyone getting hiv this way because it doesn't happen. Move on.
Yes, the risks for acquiring hiv are very clear. Unprotected vaginal sex, unprotected anal sex or sharing IV (injectable) needles. Anything exposed to air like a tattoo needle will not transmit the virus since air inactivates it.