Am working with a company trying to get their website to page one on Google.co.uk - the payments to me don’t start until their page is on page one. I now see the website on page one, but they see it on page two, also some others I know see it on page two as well!
Google search results are quite deceptive, because they depend on a lot of factors. For example, your location might make a difference. And if you are logged in to Google, your search habits will have been tracked and Google will give each person different results based on their search history. That is, Google’s algorithms are making decisions on what to show you based on what they think you are interested in.
And what does being on page one mean? For a specific key word or phrase? Or for the name of the company? (If their site is about cars, their site will never come op on page one if you Google something like ‘garden gnomes’, for example.) It’s a very wooly area, so you need to set some parameters for it to mean anything. E.g. your goal may be to get their site to come up on P1 of Google when you type their company name into Google. Make sure they are logged in to their Google account first, and get them to visit the site a lot, too!
What results, a page one ranking? That’s meaningless, what matters is the resulting traffic and how it behaves on site. I could get a page one ranking tomorrow for the phrase "blue cats like to drink horlix’ but what would be the point? Did you establish with your client what the money phrases are?
I’m curious how you’re doing SEO but you don’t know why Google results differ depending on how you’re viewing them?
If you log in with Google (Gmail) don’t try to check your website, for it will really sees a lot of differences. Try logging out your Gmail account and search for the result. If failed to do so, maybe they are trying to cheat you.