A balanced headphone connection is not the same as a balanced connection between an amp and source for example.
The balanced connection on a headphone, with a four pin XLR plug in your case (I have a balanced headphone with two three pin XLR connections), is designed to separate the left and right signal to your ears, claiming that this improves the sound compared to a single jack plug for both left and right. I don't think most people or manufacturers are convinced this is actually true.
https://benchmarkmedia.com/blogs/application_notes/audio-myth-balanced-headphone-outputs-are-better
Why Balanced Headphone Amps? | Page 8 | Headphone Reviews and Discussion - Head-Fi.org
If you haven't bought the balanced cable yet I'd stick with the 6.35mm (1/4") jack plug. The cable should be cheaper.
A balanced connection, for amps to CD player for example, is based on the idea that cables add noise to the sound so I understand. Apparently they do but only over relatively long distances, not for the meter or two that we use when listening. So balanced in these circumstances is probably also unnecessary.
The SINGXER SA-1 seems to be an amplifier only. I'm not familiar with a Mac Mini. I understand it is a computer so can be a source of digital music and have some software DAC, so out of it comes analogue music - is that correct? The output seems to be the 3.5mm headphone socket so yes, use that to twin RCA plugs. I think it's worth trying this to hear what you get. If not satisfied, look at an external DAC with USB input.
It's often said that you can better a computer DAC with a separate one. That Topping D10 may be such a DAC. A USB from your Mac Mini to the D10, and, according to the thread linked above (post 16), the Topping comes with XLR to 1/4" jack cables. Amir says that with balanced you get the 'benefits of balanced line output (main one being much higher immunity to ground loops)' so it must be true.