If you give yourself the user agent of a terrible browser such as IE5, or if you give yourself the user agent of a less popular web crawler, a lot of companies won't bother to track your identity as it would be considered a waste of resources. I'm speaking as the minion of a company that deals in such things - for instance, my company won't track you for advertising purposes if you are running Linux. No profit in it!
What happens if I use Linux while browsing at home and Windows while browsing at work? How does your company handle this? I can see a couple different scenarios and am curious which is closest to practice.
1) Track data while at work. Display only at work.
2) Track data while at work. Display at home and work.
3) Track data at home and work. Display at work
4) Don't track data at all.
Of course there's a few cases I missed but from what you said I don't see the reason they'd track me at home and display at work or any other various combinations excluded.
If I understand your question correctly, the answer would be 1. In most cases, they're doing cookie based tracking and you wouldn't have any crossover unless it was site specific retargetting and you've logged into an account on both platforms. If there's any crossover, its because you have the same browsing behaviors on both platforms.
