DC Thump-like noise with Isolation Transformer
There can be a couple of reasons why you are getting a DC thump when connecting the transformer to the source or destination.

1) The output has a permanent DC offset present.  This is often a common problem with older analog audio equipment having a bipolar power supply - the bipolar supply allows all of the audio stages to be DC-coupled and offset voltage at one or more of the op-amp stages is propagated through to the output.

This type of offset voltage is usually quite low (several mV) but can get to be quite high if there is a failure of some sort within the equipment.

The way to fix this problem is to measure the DC offset so that you know the polarity, then install a good quality electrolytic capacitor in series with the signal and a bleeder resistor from the signal to ground (to charge the capacitor).

2) The equipment runs from a single supply rail and the output is capacitively-coupled without a bleed resistor to ground at the output jack.  This is a common problem with older, inexpensive consumer-grade equipment.  

The problem is that the capacitor charge bleeds to zero when nothing is connected to the jack, and thus there is a sizeable DC offset present at the jack.  When you connect your load to the jack, the capacitor charges and the DC offset settles down at zero.  But there is a thump while the capacitor is charging.

The way to fix this problem is to add a discharge resistor in parallel with the jack so that the capacitor charges immediately when power is applied.  This resistor would normally be somewhere between 10k - 100k.

Do note that with this type of equipment, you will always get a DC thump when the equipment is being turned ON and may get a thump when it is turned OFF.