Hello!
There can indeed be fluctuations in the rankings, as Alvaro has indicated, and I agree that setting up a campaign to track your progress if a top idea.
There can be a few reasons why the rankings might look different when you do a manual search, but it sounds like you have combatted the main one by running manual searches when signed out of your Google account and in an incognito browser to avoid any personalised results skewing the rankings.
However it's worth noting that even if you're logged out of your Google/search engine account other elements, such as geography and search history can also influence ranking positions. So, there can be a lot of variation in what different people, searching from different computers/locations, might see in the rankings.
The tool runs searches from a variety of IP addresses and IP blocks using non-personalized, search history/location-agnostic requests. In our experience these have provided the most accurate results, showing what the "most" users see, though we know there's still quite a bit of room for fluctuation!
If you're still stuck, please do pop us a message at support with the keyword and URL so we can take a closer look, help@moz.com.
Cheers!
Jo