First of all, it's a rather large download, so you're probably going to close the website as soon as you click on the download button. Second of all, to consume the product in this case, you have to install it. And yet again, after you do so, if you get greeted with the "donate" window right away, you're going to dismiss it because you still haven't tested out the product.

So, what you need is a timer, something that says like "after 30 minutes (or an hour, or two hours) of usage, display the window", but that would require the OS to make calls to external servers without the user consent, and, because we are talking about a Linux-based operating system, people would be complaining that this is a a privacy violation.

Not necessarily. It's not like you expect the buyer to do a careful analysis of what it's worth before they pay. You can usually decide this sort of thing based on very quick impressions. Also, there's the aspect of it just seeming nicer to ask after the download has happened. Then it's clear that you already have the product, now it's up to you to decide what to pay for it, if anything at all. Here people have been tricked into thinking they had to pay and begrudge the author.

Really? On most sites that I visit, I 'Save As' every link that I care to download, so that there is no separate tab to close. (But maybe you were referring only to this specific site.) Maybe the solution is just to make sure that there's more of interest on your download page than just the download button?