A NBA season is 170 days long. So, the cost of a prorated minimum salary is: (number of days)/170. The luxury tax hit is also prorated.
When you look closely at the situation, you also had to look at the waivers rule. A player stay 2 full working days on waivers and is still paid by his team during that time.
For Hairston, each day cost $4332 in salary and $4856 in luxury tax. He will break the $50K guaranteed after 10 days on the roster. To cost nothing to Spurs, he must have cleared waivers on November 5th (included). November 5th is a Thursday, so 2 working day before is November 3rd. The latest Spurs can keep Hairston for free is November 3rd.
And if Williams deal is fully non-guaranteed, the deadline to waive him for free has passed. Even if Spurs waive him today, he will clear waivers on Tuesday that is the first day of the season. Williams will at least cost $4856 in salary and $4856 in tax. It could have been a hint that Williams will be kept but Spurs waived Hairston just after the deadline last year while his contract was fully non-guaranteed.
I've been long but I think it's more interesting to know the rule instead of only the answer.