The Irishman's first Dundee derbies were in July and August when United won 3-0 on each occasion and the Dark Blues took a while to get going following their late call-up to the top flight.
Now, though, Dundee have won three of their last five in all competitions to cut the deficit at the foot of the table and Dillon knows United will have to be at the best when they cross the street to play.
Dillon said: "I knew it wouldn't take them long to start picking up points - I didn't doubt that - and I'm not really surprised that they have picked up points lately.
"They've got some really good players, they've got a great backing from their fans, no matter where they go.
"They've got quality all over the pitch. It's just a case of hopefully getting things happening for them.
"Obviously we don't want that happening on Sunday. We'll be trying to make sure we can get three points for ourselves and forget about them."
Meanwhile, Dundee boss Barry Smith has told his side to show their ability in Sunday's derby.
"The mood's always good around the dressing room and everyone's looking forward to the game, but it's a game we have to take part in," Smith said.
"(It's about) a lot of hard work and making sure we play with a cool head. It's easy to get caught up in the atmosphere, but it's the ones who don't get caught up who will stand out."