HomeKit stores data in a database on your iOS device and other HomeKit apps have access to them. For example, if you change the name of an accessory in Apple’s Home app, the new name will appear in Home+ too.
Some changes are stored internally by apps. For example the list of favorites in Apple’s Home app is stored internally. Therefore other HomeKit apps do not know which accessories are favorites.
Home+ also stores settings internally, like the accessory icons, the sort order of accessories, automation folders and the list of favorites. Those settings are synchronised automatically via iCloud with your iOS devices. This means that if you change the icon of an accessory on your iPhone, the new icon will also appear on your iPad.
Unfortunately other people in your home do not have access to those settings because they use a different Apple ID. But you can manually share the settings with others by using the Share Settings feature, which is available in the app settings.