`mount -l` shows a filesystem of type `overlay` for each browser (in my case, chromium, chrome, firefox). Range from 50MB to 200MB. I have it to sync to disc every 15min - so I reckon it empties out the ram whenever it syncs. I've never had a problem (8GB of ram on the machine I initially installed it on) so I haven't watched to see what the max size is. The developer [1] is great - issues are resolved very quickly.

[1] https://github.com/graysky2/profile-sync-daemon