Why rankings in Google may not match
Except for general reasons rankings may not match with SERP there are some peculiarities in Google that must be taken into account while checking rankings manually.
Location
A search location must be the same you've added to the project. While checking manually Google automatically defines your region using IP address, location and search history. The location is displayed at the bottom of search results page. But it can include city district, zip code and other additional address information that Google API doesn't support.
For proper check there must be the very region you've added to the project (e.g., "New York", not "New York, Manhattan, 10060") and corresponding country. To check rankings in Google manually use AdPreview Tool located: https://ads.google.com/anon/AdPreview.
Spellchecking
All search keywords in Google are checked for misspelling and typos. By default both in Topvisor and in Google spellchecking is enabled. If you disabled spellchecking in the project Settings, make sure you check rankings for a uncorrected keyword. For that press on the original keyword after the phrase Search instead for under the search bar.
How to change spellchecking settings →
Filters
SafeSearch in Google can be enabled. While it's on, SafeSearch removes explicit content: nudity, violence, gore and others. If you use SafeSearch in Google, make sure you've chosen the same filter in the project.
Front servers
Google uses servers located worldwide to process search queries and provide search results as fast as possible. There are different front servers in the USA, Europe, Russia and other regions.
Google tries to deliver search results from the server closer to a user's location. A user from New York will be assigned to American front server, and a user from Moscow — to a Russian one. But different front servers can deliver different search results, and users from New York and Moscow checking SERP for a keyword with the same search engine settings (language, filtering etc.) may get different SERPs.
Usually a front server is assigned to a user, and if you refresh a page, search results don't change. That's because Google caches search results (caching session) to make Google search work faster. But if you open a new window in the private mode, clear all browser cache and cookies or use another browser, search results can change. It means that Google rerouted you to another front server.