Bitmap changes color after editing

You must embed the colour profile as a matter of principle.

Whichcolour profile to choose for your work?

In circumstances where users down the line may not use colour management or for web use then sRGB is generally considered to be the de facto working colour space since it is most likely to give a reasonable result..

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

What are Photoshop’s Edit > Color Settings? 

What is the images’s original Color Space? 

Please set the Status Bar to »Document Profile« and post meaningful screenshots of the original and the untagged result. 

In which application does the appearance differ from the original – in Photoshop or some other application? 

If that application is not color-managed it is naturally irrelevant as far as color appearance is concerned.