Have a listen to the previous word in the Pronunciation database - tabhaigh. It has the same spelling as tabhair, and it's first syllable is pronounced with the "ow" vowel sound.
For a language that people keep insisting has consistent pronunciation rules, there seem to be a lot of exceptions.
I'm intrigued, because this doesn't seem to be dialect variation like many of the other comments on the course; it's [au] ([av] in Munster?) across the board for tabhaigh, and some range of back-rounded mid-high vowels for tabhair. Also, since the latter is tugann and thug, I wonder if ultimately there's an underlying u-ish phoneme in the word, and its -abh- is just an orthographical mismatch (either because it hasn't been revised with the standard, or the underlying phoneme was formerly au-ish, as with tabhaigh).
It's a wonderful exercise for English speakers, though, experiencing the perfect storm of sound, spelling, and dialect that English learners must go through. :P