Basically, items in the parallel DOM register themselves as dependants of 'keypaths', so a {{user.name}} mustache depends on the value of user.name. If you do ractive.set( 'user', { name: 'Bob' }), Ractive scans the dependency graph to find items that may need updating. The mustache will compare its new value to its old value, and if it has changed it will update the text node that it is mirroring.

I'm not intimately familiar with how React updates happen so I can't comment on how similarly we're doing things, but it looks like we have the same kind of approach.