I'm definitely a driving instructor - I'm way too bad at following corporate rules to be an examiner - they'd sack me within days.
And all my students will tell you I'm lovely - otherwise they'd get a zap from the cattle prod to keep them in line.
And the answer to your question is slightly complex as it depends on exact timings and whether the third party follows the correct path around the roundabout, how they position the car, what exact speed they enter the roundabout etc. I can only control their expectations of my actions with my signal, my course and my speed - I need to make sure that all of these give a clear sign of my intentions at the roundabout. After that I just have to judge their reaction to my approach.
The only time in principle that a lack of right signal would be a problem is if they got to the roundabout a little ahead of me. Then I might assume they are going ahead, start to enter, then have either a collision or a near miss. But I am weighing their speed and position - in particular speed - if they are going ahead they would probably be going faster. If they are unusually slow, alarm bells will be ringing that they are turning right without a signal, and speed is duly reduced until I'm happy I know what they are doing.
If we are arriving at about the same time, we should be able, on all but the smallest mini roundabouts, to do an offside-offside turn about each other even if I am not suspecting the unsignalled right turn. But I'm also suspicious of the people who cut the centre of mini roundabouts. So this is where closely watching position pays off. Now my first warning of trouble is likely to be a deflection towards my left, again speed reduction until certainty established.
If I'm arriving slightly ahead of them, I take control of the situation by being on the roundabout ahead of them (but still monitoring their speed on approach to ensure it's consistent with them giving way to me correctly).