Dishwasher on Shabbat

Hi,
I have a question about using the dishwasher on Shabbat.
I follow the Tzomet permit and I have a Tzomet clock, and one of their instructions for using the dishwasher on Shabbat is to put a stopper in advance where the liquid comes out and throw the tablet into the dishwasher first.
The reason for the instruction that you load dishes in the dishwasher and then close the lid is to prepare a dish and then the liquid and tablet can be boiled on Shabbat.
But I often load dishes into the dishwasher after I've washed in the sink, so water falls on the dishwasher door and then I close the dishwasher door, and the water could boil on Shabbat.
I thought it was similar to cooking meat with a little sauce, which was negligible and had no meaning.
But I would be happy to hear the Rabbi's opinion on the matter?