This is a cool idea and nice drop-in for most homepages with a custom tweet button + share count-- great job to the devs that put it together! However, it appears to use the REST API's search endpoint to count the shares, which is focused on relevance and does not guarantee completeness [1]. This will probably will not be very accurate in most cases, especially for URLs with many thousands of tweets in between their periodic searches. Unfortunately, the only way to guarantee completeness is to use the Streaming API, and if your needs extend past the default 400 keywords allotted, you'll need to pay Twitter/Gnip.

1. "Before getting involved, it’s important to know that the Search API is focused on relevance and not completeness. This means that some Tweets and users may be missing from search results. If you want to match for completeness you should consider using a Streaming API instead." https://dev.twitter.com/rest/public/search