Brown spots on Adonidia. Need to be treated ?

[PalmX]

Just got these brown spots on my potted Christmas palm when bringing it in for the winter. 

Can't remember if these need to be treated with Copper Fungicide? Or will a Dawn and Alcohol solution work just fine? 

If I do nothing, will these spots continue to spread since the palm is inside and no longer getting wet?

 

[Almisa]

Bacterial/Fungal infection. Overwatering probably prior to bringing inside. If potted, make sure it has great drainage but slow down on the watering for a minute, except you have to immediately treat the tree with diluted peroxide to the soil to halt the spread of infection and eventual root rot. Copper Fingicide will not correct the condition but it won’t hurt to apply it. You will lose the leaves in the picture. How does the rest of the tree look?