1. HIV in essence is a sexually transmitted disease.
2. Potential risk for HIV contraction are vaginal or anal intercourse with out the use of condoms. Also, sharing needles to inject drugs with people of questionable serostatus is an exposure.
3. Tattoo and peircing needles can't infect with HIV because if it may contain infected fluid, it is in contact with the environment and not in a vaccum as it is in a syringe and that renders the virus uninfectious.
4. The point of an ultrasonic cleaner is to sterilize from bacterial, fungal or other living microorganisms infection.
5. No risk whatsoever. No scope for transmission. Not even a single recorded case in the history of this disease. No testing would be required.
The whole point of the ultrasonic cleaner is to disinfect the tools. It's completely irrational to think that there would be any contamination left after using it.
This answers all of your HIV questions, and if you can think of any more just reread about the 3. You had zero risk therefore testing is irrelevant to your situation because you had zero risk. HIV is a fragile virus, which is instantly inactivated in air and also in saliva which means it is effectively dead so it can't infect from touching, external rubbing or oral activities. It doesn't matter if you and they were actively bleeding or had cuts at the time either because the HIV is effectively dead.
Only 3 adult risks are the following:
1. unprotected penetrating vaginal with a penis
2. unprotected penetrating anal sex with a penis
3. sharing needles that you inject with.
The only way to get HIV is if you did one of the 3. The situation you describe is a long way from any of these 3.
Even with blood, lactation, cuts, rashes, burns, etc the air or the saliva does not allow inactivated virus to infect from touching, external rubbing or oral activities. Doctors have calculated the risk from what you describe to be less than that of being hit by a meteor, therefore no one will get HIV from what you did in the next 40 years of your life either. The above HIV science is 40 years old and very well established, so no detail that you can add to your encounter will change it from zero risk.
If you didn't have one of the 3 then you are just worrying about your own hiv theory - which is unrealistic for you to think that can become reality - so you should move on back to your happy life instead.
No one got hiv from tattooing, otherwise the parlors would be regulated to be run by medical staff..