Intrusive 'r' (linking 'r')

'Csaba (r) is right' - One of my British tutors used to say. I always wondered what that 'r' was doing there. It is an intruder and mostly appears between a schwa that ends a word and the following vowel that starts a new word. Native speakers do that without noticing.

Vanilla (r) ice

Put your umbrella (r) up

That dog I saw (r) over there.