In the first of these posts the model sentence is wrong.
I will carry out a deal tomorrow ,but when i meet you later tomorrow,I will not think that you know i did (tomorrow/the same day)
However, the answer is almost certainly I did it the same day.
"Whatever day I meet him next week I'm sure he will tell me Todd is doing it on that day."
"Whatever day I meet him next week I'm sure he will tell me Todd is going to do it the following day/the next day."
"Whatever day I meet him next week I'm sure he will tell me Todd did it the previous day/the day before."