Since I am using almost the same tipping bucket rain gauge, let me try to explain how it works:
The top of my funnel measures 109 x 49 mm = 5341 mm2 (square millimeters). For now, let us not worry about the rounded corners of the funnel.
If it rains 1 mm the funnel will collect 5341 mm3 (cubic millimeters) which is 5,341 cubic centimeters equal to 5,34 milliliters. This is difficult to use for calibration so let's try with 10 mm of rain which then equals 53,4 milliliters or 0,53 deciliters of water.
So, you pour 53,4 milliliters of water into the funnel, not spilling any and you count the number of bucket tips. In my example, when I do this, the bucket tips 30 times. So if the bucket tips 30 times during a time period, it has rained 10 mm during that time. Or, the other way around: One tip of the bucket = 10/30 = 0,33 mm of rain.
Do not worry about the size of the bucket inside. What matters is how many times the bucket tips for a given amount of water. It is the area of the funnel which is important.
When it rains 1 mm an area of one square meter will receive 1 liter of water but the little funnel will only receive 5,34 milliliters as explained above.
Now, if you really want to be accurate, you should take away the area of the rounded corners. But that will be less than 0,5% and there are other sources of inaccuracy.