DT and HT do not really change AR/OD/AR the same way as a change in their values would do.
OD: DT and HT change the real-time time windows of all timing windows proportionally to the change of speed. Changing the OD value from one value to another doesn't change all timing windows by the same value (for example, OD10 has a significantly smaller timing window for a 300 compared to OD8, but the timing window for a 100 doesn't proportionally change as much). Tillerino gives a different value for OD with DT/HT by considering only the timing window for a 300.
AR: DT and HT change the duration of each part of the hitcircle fade-in and fade-out animation proportionally to the speed, while changing the numeric value of AR doesn't change all parts of the animation proportionally. Tillerino gives different values for AR by considering only the total time between the moment the note starts to appear on the screen and the time it has to be pressed.
HP: DT/HT do not change how much note hits and misses drain/restore the HP bar, they just change the speed the HP bar is passively drained.