"UBS tutora" is not a common term, and in fact I have only found it in a couple of documents referring to one particular health insurance company. I think it is specifically their term. "Tutora" is an adjective, and refers to the function of this UBS or basic health unit: that of exercising "tutela", protective care. The unit consists of a doctor and a nurse. I don't get any sense that it means tutoring in the sense of giving instruction (though that may possibly be involved), but rather in the sense of a guardian of the health and welfare of staff. Specifically, its major responsibility is to monitor the implementation and operation of the company's occupational health programme. So I think "health protection monitoring" would express its function.

The following document is useful in this respect, but there may be confidentiality issues here so I'll suppress the name of the health company concerned and the URL:

"Para la gestión del contrato de prevención, el Servicio de Prevención Ajeno designa un Técnico Tutor y una Unidad Básica de Salud Tutora, que serán los interlocutores con la Empresa y quienes realizarán un seguimiento cercano de las actividades realizadas.
El Técnico Tutor del Servicio de Prevención Ajeno de [Company name], tras la primera visita técnica, realiza, de forma consensuada con los representantes de la empresa, un Programa de Actividades Preventivas, donde se especifican las actividades a realizar, su alcance y las fechas previstas para su ejecución.
Asimismo, la Unidad Básica de Salud (UBS) tutora de la empresa, formada por un Medico Especialista en Medicina del trabajo y una DUE de Empresa, establecerá, ejecutará y supervisará el Plan de Actuación en Medicina del Trabajo dentro de la demarcación geográfica de la empresa. En el mismo se especificará la actuación en materia de Vigilancia de la Salud en los distintos puestos de trabajo existentes en la empresa dependiendo de los riesgos a los que están expuestos los trabajadores, especificando los protocolos médicos específicos a aplicar así como el resto de actividades y su plan de ejecución."

So this UBS doesn't seem to provide treatment (it may do so, but that is not its primary function). It is there to ensure that the prevention plan is properly implemented.

"Staff" and "monitoring" could be included, but perhaps they could be omitted. "Staff" will be understood in context, and although monitoring is their major function, it is not the only one; they also carry out the plan as well as monitoring it. So perhaps just "basic health protection unit".