This is something that I believe has changed, but if you're counting backwards, the arrival date would count as day zero, as you say. (I believe it was at one time that the day of the call and the day of the reservation were both part of the count.)
Here's a way of looking at it - 91 days would be exactly 13 weeks, so 90 days is one day less. If you arrive on Saturday, your 90-day point would be on a Sunday. If you arrive on a Wednesday, your call day would be a Thursday.
A lot of folks have also found it to be convenient to think in terms of three months being about 90 days. So today is 6/29, and three months from now would be 9/29. Since there are two "31sts" between now and then, that means that today one could call for meals up through the 27th of September. (And checking the system, sure enough, that's what's available, and it's a Sunday.)
Hope this is helpful. If all else fails, just pull out a calendar and start counting backwards, with "1" falling on the day before your arrival.