What are the implications to devices?
And BTW, can this happen with isolated transformers?
To hell with devices------it can zap
you!It looks like what you have is an auto-transformer.
If you swap Neutral & Active on them,you will get just the situation you report.
An isolated transformer,or more correctly "isolating transformer" has a secondary winding which is electrically isolated from the primary,so that
neither side of the secondary winding is connected to Active,Neutral,or Earth.
An auto-transformer,on the other hand,is just one winding ,connected between Active & Neutral of the higher voltage (in your case,220v) source.
To get 110v ,the winding is tapped (in this case,a centre tap),& the 110v device being powered is meant to be connected between the Neutral end of the winding & the tap.
If your Neutral & Active are inverted at the transformer input,they stay inverted at the output.