from XX/XX/2018 - July/01/2018 which is a day before my arrival date. are they really strict and will I run into problems if I arrive the next day which is July the 2nd?
Don't take immigration stuff light. Nobody will let you board if your clearance has already expired. If they let you board and reach your destination you will be deported because you do not have clearance to enter a country on that day in any form.
It doesn't make a difference if it is 1 day or 1 year.
Are they really strict and will I run into problems if I arrive the next day, July 2?
This is not local law enforcement which can be strict or lenient sometimes depending upon the nature of the issue in hand. This is immigration stuff and in a different country, if they are not strict about the validity period they are not doing a good job of it. It is inconceivable that border guards will take those dates casually.