It is supposed to be either pronounced as just «у» or almost vanish. I prefer the latter, whereas this voice pronounced it. But I am quite young. I think, the sythesized voice might have been based on a voice of a speaker who is 40-50 years old and may have quite a number of habits different from mine.
Is it just how this word is pronounced, or is that true of "уй" in general?
Cyrillic "Р" makes a rolling r sound. What you should be spelling it with is П. "П" makes the same sound as an English "P".