Why did Kaka Mahajani's friend feel restless about the Dakshina? Didn't he want to avoid giving any in the first place?

Yes, initially the friend's condition was that he would not give any Dakshina. However, his experience was designed by Baba to address this resolve. Chapter 35 explains that Sai Baba asked Kaka Mahajani for Dakshina on two separate occasions—once in the morning and again in the afternoon for seventeen rupees. Crucially, Baba pointedly asked nothing of the friend. While this fulfilled the friend's initial condition, it had the opposite of the intended effect on him. After his profound experience of hearing his father's voice, being excluded from the act of giving an offering made him feel "restless in his mind," suggesting he now desired to give but was not being given the opportunity.