When building a district, I see that there are certain 'empire effects' with them.

Some I undertand (+4 Influence when at the extreme of 'Liberty' but others not so much.

Playing as the Phoenicians and then the Carthaginians - I also have +8 Food and +8 Production on my Cothons (just +8 Food on Farmers, +8 Production on Makers).

My last game, I had +15 on my Research Quarters.  That one was with the Mycenaneans and then Persians

Where are these coming from?

OK, I figured it out... the +15 science was from 5x Silver and +5 Tenet.

The +8 food/production is from 4x saffron and 4x silk, respectively...

You got it, it's from district luxuries like Silver and Saffron.  I like how they're implemented, but I'd love if the tooltip said they were "From Luxury Resources" instead of "From Empire".