I'll add this: be sure to test sync'ing a lead and when it doesn't work, check the activity log on the Lead you test with
I was having the same issue, where I set up Lead Assignment Rules(LAR) in SFDC, but they didn't seem to take effect. I checked the Activity Log for a lead test and next to the item 'Sync Lead to SFDC', there was a campaign listed, also titled 'Sync Leads to SFDC'. It was set up years ago to capture data of anyone who fills out any form on our website.
Here's the kicker: The smartlist on 'Sync Leads to SFDC' was 'when lead is created' and the rule on 'Sync Leads to SFDC' campaign was to assign new leads to a Queue and LAR were the default choice. I switched them and voila! now it works.
Weird sidenote: when I originally set up the campaign in question(not 'Sync Leads to SFDC') we had assignment by Geo territory built into the campaign and that overrode the 'Sync Leads to SFDC' campaign. I don't know why that was working and LAR wasn't, but LAR wasn't.