Could you post the family? Are either one checked as "always vertical"?

I am unable to post the family just now for rather draconian intellectual property reasons. We're still rather coy in the UK about who gets to see what, even when it does shoot ourselves in the foot like this sadly.
Could you explain please what you mean by checked as "always vertical"? They are horizontally mounted along the plane of the ceiling.

There are certain types of families which have a checkbox in their properties which says "always vertical". If you used one of those, then nest it into a face based host, it will keep orientated as inserted. This might cause the behaviour you're seeing right now. Although it's hard to say without the actual family. Btw: is this really something to be worrying about?? Doesn't seem that special to me...

It is important as the RI symbol shows the location n 2D of a remote indicator LED for the smoke detector. It is used to show if the detector in the riser is the detector causing the system to go into alarm.

We have fixed the problem by amending the symbol which had previously consisted of a symbol family of the smoke detector (the round target looking thing) with the long dotted line and the RI in a circle as a separate nested family.
It appears that the constraint in the main family which rotates the annotations consistent with the 3D model (Which in turn rotates in view as the viewport requires it to.) does not apply to families nested within the first symbol family. So de-nesting this family meant that the symbol came under the influence of this rotational constraint.

Now the whole thing rotates with the viewport allowing it to remain in the correct place and not confusing the contractor further than my electrical designs usually do.

Thank you for your help in this matter! It is a bit of a bind having to provide a 2D output in Revit. This is our first project and we really want to show off our 3D abilities. We have spent a year learning how to use this thing and our contractors are not interested in taking the Building Information Modelling (BIM) information. They want to stay in the 20th century.

One hurdle at a time...