There are are a few important steps for setting up Lab Monster Toolkit with SF6.
If you want the toolkit to take player 1 and 2 slots and have your controller be player 3, first unplug your physical controller. Then boot SF6. Go to the toolkit and set player 1 to UI input, and press the start button in the UI for player 1 and check the turbo box. Click back into SF6 and watch the intro sequences get skipped. Once you are sure SF has read player 1's input, do the same for player 2. Then disable player 2, plug your controller in and set player 1 to mirror source input.
I have found that the game logic for SF6 can vary slighty depending on the computer it is running on. On my desktop PC a frame is perfectly 16.6667 ms but on my laptop it runs slightly faster at 16.23 ms. If you want the toolkit frames to perfectly match the games frames, I recommend creating a training sequence with a button hold for 90 frames, followed by inputs of length 1,2,3,4,5,6,7,8,9 and 10 frames (here is one I made). Boot the training mode in SF6 and play the sequence. Tweak your timing numbers as needed to match the frame values. This frame length value was added in version 0.0.8.4, so upgrade if you don't have it.
Video showing setup process.