Upvote:6
The Mexican embassy is wrong, days in Ireland do not count toward the 90-day limit in the Schengen area. There are subtle rules on how days are counted and how the limit works with visas from Schengen member states but since Ireland is not in the Schengen area, it does not make sense to consider all this. On August 25, you will simply enter the Schengen area for the first time with a full 90 days of potential stay.