Why do I want to urinate when I touch water?
FIRST PART:
I am writing this answer with an analogy.I have analogised your question to a childhood habit developed by our mothers-when she would want us to urinate all she had to do was to take us to the toilet and make a &quot;siiii&quot; &quot;siii&quot; sound to mimic the sound of running water(more or less)
Since I have analogised in that way I think the third hypothesis (referred in your question)is more apt.
SECOND PART:
What fascinated me more about your  question was your comment-&quot;I'll also be interested to see why the people will learn to have desire to urinate at the sound of tap water. Is there any reason that for that? – Hosea Jul 14 &quot;
Indeed there is because we still have our mirror neurons
[SOURCE]
What I wanted to understand is if mirror neurons contributed to Pavlovian reflexes.The answer was yes
Furthur I could find out from sources that the micturition process has centres in the brain stem which are controlled by higher centres in the brain.One of them was the &quot;medial frontal cortex&quot;.
Read the following article:

The Pontine micturition center (PMC, also known as Barrington's nucleus) is a collection of neuronal cell bodies located in the rostral pons in the brainstem involved in the supraspinal regulation of micturition. When activated, the PMC relaxes the urethral sphincter allowing for micturition to occur. The PMC coordinates with other brain centers, including the medialfrontal cortex, insular cortex,hypothalamus and periaqueductal gray(PAG). The PAG acts as a relay station for ascending bladder information from the spinal cord and incoming signals from higher brain areas.[source]

From the outline in the following lines I could conclude that there are mirror neurons in this region which 'may' be involved in the micturition control:

Yoshida et al. [26] recently recorded from neurons in the medial frontal cortex, some of which selectively responded to self or observed actions within a social context
[source]

Although research has confirmed that mirror neurons contribute to Pavlovian reflexes no such pathway has yet been discovered which can directly help us to confirm  and understand its relation to urination urge in contact with water.