Answer:
Rashes sometimes accompany viral infections and fevers, especially in children, and can be an indication that urgent medical examination is needed. Rash can be an early sign of serious infectious disease, both viral and bacterial, such as in bacterial infections with toxic shock syndrome.
Specific viral rashes have names such as chicken pox and rubella (German measles) and are often identified by their characteristic appearance of the rash and other symptoms. However, often the type of rash or other symptoms do not allow that specific a diagnosis to be made. So, the term "non-specific virus" is used to indicate that there have not been laboratory studies or specimens collected to grow (culture) and identify the exact virus causing the symptoms (which have been determined to not likely be characteristic of or typical of known specific viral rashes). These studies are typically not needed or ordered by the physician since the most common viruses to cause rash and cold-like symptoms are treated much the same way even if the specific type of virus involved is known. It is different in the case of bacteria and bacterial infections where the exact organism must be identified to prescribe the proper antibiotic to get rid of the bacteria.
Antibiotics, however, do not work to treat viruses. When no bacteria have been identified and no allergic cause of the rash has been found, then the presumptive working diagnosis is often "non-specific viral infection."
Responding to your addendum to the question on the discussion page asking why contact precautions were given, it is likely that these precautions are to be taken since the specific virus has not been identified, and some viral illnesses that can cause rash can be especially dangerous for children and pregnant women and the developing fetus. German measles, for example can cause harm to the developing baby.