很有 pronounced rather like hěnyòu instead of hěnyǒu
The obligate tone sandhi for consecutive third-tones are rendered as follows:




Phrase
Before
After




很有品味
3334
2234


很有才能
3322
2322


很有辦法
3343
2343




In particular, the 333 -&gt; 223 change in 很有品味 is explained here.

Possible facultative tone sandhi in 很有 in quick speech include:

For all 很有XX examples: blurring of tones (quasi-neutral, as explained here; to avoid confusion, let us not use the dotted tone letters normally reserved for real neutral tones, and let the one-lettered pitches reflect their brevity) in the presence of stress on XX out of contextual need (as explained here).
For 很有品味: a blurry rising trend for consecutive de facto second-tones, as explained in the 葡萄牙 example here (perhaps something like ˦ ˥).
For 很有才能 and 很有辦法: a blurry dropping trend (perhaps something like ˧ ˩).


What you seem to be implying is that the teacher pronounced 很有, in quick speech, with a go-up-and-down pitch change, i.e. ˨ ˧˩. Now, is this possible? If you are absolutely sure there is no mishearing or mislabelling on your part, then I think the teacher did not conform to standardised Putonghua well (i.e., this is a mispronunciation on their part). However, I am not entirely sure about your labelling 有 with two tone letters – is it worth that many, especially when it is expected to be blurred over? After all, we are treading on very thin ice here – it is very hard to capture every nuance of facultative tone sandhi. Unless I hear the teacher's audio, or an audio from an online source (e.g. YouTube) that you believe is close enough to the teacher's, I cannot provide a definite answer.



Edit
Now that we have made clear this was normal-paced, I am starting to suspect this is similar to the case of 比較, where some people say it as (bǐ jiǎo -&gt;) bí jiǎo instead of the conventional bǐ jiào (see here for more examples). The link contains examples of non-dictionary readings.
I also found evidence where 有 may be pronounced as yòu: see here. Its use is relatively limited, i.e., when acting as a loan word (通假) for 又 in classical Chinese*, or when denoting numerical remainders (e.g. 七十有七人), both of which are not the applicable to 很有. However, 教育部重編國語辭典修訂本 claims yòu and yǒu are interchangeable (I for one think this is rarely practised in real life). At any rate, the teacher's choice of pronunciation is not mainstream. I also believe this is caused more by the polyphony of 有 than facultative tone sandhi during quick speech.
* Also supported by 余培英（2012）《多音字學習手冊》。北京：商務。