I would believe that you would be safe for the time being, as yo would have a viable defense to the forclosure (you are not delinquent), but I strongly urge you to consult with a bankruptcy attorney as there may be avenues through the bankruptcy programs to save the house going forward, reduction of overall debt which increases debt to income ratio, and other helpful matters.
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I am not licensed to practice in IL so can not give legal advise, but you are obviously losing sleep over this, so let me give you some practical advise: if you received a written statement reflecting the amount necessary to reinstate the mortgage, and you timely paid those funds, you are probably safe.
The "however" is: without reviewing the mortgage document and the letter, even an IL attorney would not want to give legal advise. You should confer with an attorney in person with your documents in hand for review.
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Be sure to keep the letter regarding the amount needed to reinstate, and the receipt for the funds you sent to reinstate the mortgage. Also, I would recommend going to the company where you received the certified funds and get a copy of the cashed funds. This is proof to show that you are current through the date on the letter.
You should also be saving funds to pay the mortgage payments that are coming due each month. If you paid an amount to be current through June, then you will need to be prepared to be current through July. Carefully read the letter they provided to ensure that the amount you paid brought you current through June.
Follow up with a foreclosure defense attorney if the mortgage company will not reinstate your mortgage.