looking at transformer equivalent circuits I don't see reflected capacitance. Reflect impedance, reflected leakage inductance, but not capacitance. Do you have cite for this?
@jpjones3318 Transformers are called that because they transform impedance. They do not isolate it!
So a load on the output of the transformer very much affects the source on the input side. This is part of why the transformer must be loaded correctly. Incorrect loading of the transformer can have other effects too- for example all transformers have inter-winding capacitance. If the transformer is too 'lightly loaded' (output load impedance is way too high) the inter-winding capacitance will begin to affect frequency response, perhaps manifesting as a hump in the frequency response rather than being flat.