That's exactly right.
If you play TIE all the time, and you're still in the cup, your enthusiasm right after your games can be at the top of the scale, but then it diminishes each day until you play TIE again or hits 5. The highest I think I've ever had my enthusiasm on game day is an 11.
However, I'm not certain, but it seems that enthusiasm is valid in Private League games, which means you can play your PL games with enthusiasms much higher than you can play league/cup games.