Based on my observations, your theory appears to be correct. Spinning a disc that is on a gym that your team controls will give you an extra item. That item will be indicated by the colored background that matches your team's color.
For reference, I am on Team Mystic. When spinning the disc at Valor and Instinct gyms, I did not receive a "special" item, but I have at the Mystic-controlled gyms I've spun.
This is also being mentioned in other places, such as this thread:
To confirm my suspicions, the team bonus items are highlighted with team color, correct?
It seems so, yes. My team bonus was highlighted red, and I'm Valor.
Flavor thing: as a Mystic player, my team bonus text and background on the bonus item are blue. Can Instinct and Valor confirm their text/background colors on bonus items?
yes instinct here, yellow.
Valor, the bonus item text is red.