When an item has variations, e.g. size/colour, and you select a variation, the screen is replaced by a default blue/grey item with selection boxes, including titlebar. Is there a way to correctly theme this entity to match the rest of the app?
The same holds true to the onpress event within the list of items if you have a "more" menu section. It will be a blue onpress colour to indicate selected.
The modal screens you describe (variation selection list or the "More.." tab list) are default iOS table screens and cannot currently be themed (Mobile Engine 5). The colors appearing there are very similar to what you have in the default iOS settings app.
If you want to be able to edit them, please submit a feature request in Appixia Jira.
What the engine does support, is theming the titlebar color only. This way you can have a titlebar color which is consistent throughout your app (in case you changed the default one). Although this is supported by the engine, Appixia Dashboard still does not support entering these colors. There's an existing issue for this, you are welcome to follow it and see when it's implemented.