Q: My practice rents space to another practice with employees. They use none of our supplies and operate as a separate business. Is my practice responsible for OSHA training for their employees?
A: If there is no employer-employee relationship, there is no OSHA obligation.
In the case you describe, you would be responsible for the OSHA training for your own employees. The owner of the practice who rents from you would be responsible for his/her employees.
That is assuming that the employees of the rental practice perform no services for you, and you do not pay the rental practice for these services. In that case, the rental practice employees could be viewed as contract employees and you would have a shared OSHA responsibility.