The articles may be broadly correct in most parts. I did not read them all, but look at example 1 in the first article, it discusses how to calculate the maximum contribution, not when to make it.
You may want to review publication 969 and the instructions for form 8889.
https://www.irs.gov/pub/irs-pdf/p969.pdf
https://www.irs.gov/forms-pubs/about-form-8889
In particular you should see from the forms and worksheets that your contribution limit is determined by the type of coverage you have on the first day of each month (single HSA-eligible HDHP, family HSA-eligible HDHP, or non-eligible coverage) but there is nothing on the form to specify what date the contributions were made.
The bottom line is that what counts on your tax return is the amount of contributions, and not when they were made.
