Step 1: Recall what a tipping bucket gauge physically records.
A tipping bucket rain gauge tips and sends a signal each time a fixed small volume of rain has collected, and the time interval between successive tips is logged. Since intensity is depth of rain divided by time, the tip timestamps directly give the rate at which rain is falling at any moment, so Statement I is correct.
Step 2: Recall what a natural siphon, float type gauge physically records.
This gauge uses a float that rises with the water level in a collection chamber and drives a pen across a rotating chart, producing a continuous trace of cumulative rainfall against time. That cumulative rainfall versus time trace is precisely the definition of a mass curve of rainfall, so Statement II is also correct.
Step 3: Cross check by contrast.
The two instruments are complementary rather than doing the same job, one reveals intensity peaks and the other reveals the running total, which confirms both descriptions are accurate rather than one being a misattributed feature of the other.
\[ \boxed{Both Statement (I) and Statement (II) are correct.} \]