I tried changing the settings mentioned in the link evilbadger shared but I still see the emails that I deleted on my 920, on my laptop.
As to how I was able to access the m.google.com page, here's what I did:
1. Opened IE10 on my laptop.
2. Alt+T-> F12 developer tools.
3. In the new window that pops up, click tools->change user agent string and select Apple Safari (IpAD).
4. Went to "https://m.google.com/sync/settings/" exactly (without double quotes of course), and it opened the correct mobile version of the page. Signed into my Google account
5. I selected Windows Phone and selected the box adjacent to "Enable "Delete Email As Trash" for this device." and saved these settings.
Even after I do this, emails deleted on my Lumia 920 still show up in my Gmail inbox on my laptop.