I looked and looked on Mrs. Meyer's website to find the answer to this question, and could not. Therefore, I called their customer service number and asked. The answer, according to Mrs. Meyers, is no, you do not need to rinse off this product after you use it to clean your tile floor.
Of course, since the all purpose cleaner is concentrated you will need to dilute it per the instructions in some water before you begin mopping with it.
On the other hand, I have often read that after mopping ceramic tile that rinsing your floor is important. The reason given is that the grout can absorb the cleaner, which will then attract dirt, and get stained if you don't rinse.
Of course, if you have sealed your grout this is less likely to happen anyway, because it will prevent or at least lessen the ability of the grout to absorb cleaning solutions.
I would love to hear from other people in the comments sharing their experiences with this particular all purpose cleaner, or in general, of whether you rinse your tile floor after mopping it, and what you have experienced, especially in regard to your grout.
There frankly is probably not a right or wrong answer, but instead what seems to work best for you, your floor, and the amount of time you want to spend mopping and cleaning it.
I hope you enjoy this gift, and stop by again soon!
CAUTION: This website is provided for informational purposes only. It is provided as is, without warranties or guarantees. Some stains and messes just won't come out, and are permanent. Further, some cleaning methods can harm your item, so if what you want to clean or launder is sentimental or expensive call a professional. See disclaimer of liability for more information.