Well, technically, no one (including your employer) can contribute to your HSA when you are ineligible.
However, the way the calculation work is that your annual HSA contribution limit is calculated based on your type of HDHP coverage and the number of months are are covered (exception - if you are covered on December 1st of the tax year, then you can use the full annual HSA contribution limit).
Got that? Note that nobody askes you WHEN the contributions were made, so it's all the same to the 8889 if you (or your employer) made the contributions in January when you weren't covered or in December when you were. And note that if you were covered on December 1st, then you were retroactively covered for all year (in essence).
So look at what your employer will have contributed by the end of the year, subtract that from your calculated HSA contribution limit, and that is how much you can contribute.
I know this seems to fly in the face of the IRS wording. Thou Shalt Not Contribute If The Taxpayer Is Not Eligible, but in practice, that is not how it works in the calculation - what matters is what you end up with at the end of the year.
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