Yes, you are confusing it with that. Once your leveland gathering statand a certain stat breach a certain threshold, the jig/chop/strike location during the approach phase (phase 2 of the minigame) will always be in the same location.
As far as I know, nothing affects what item comes up except where you select during the first phase of the minigame (the 'aim' phase). Even if something does affect it, nothing guarantees that you'll get what you're aiming for.
Edit: Found the source (1.17 patch notes)
The approach phase is phase 2 of the minigame (it says 'approach' above the jig/chop/strike box).[dev1039] When the three below conditions are met in regards to the grade and difficulty of a gathering attempt, the "sweet spot" of the approach phase will be in a fixed location.
1. Class rank
2. Values of VIT for miners, STR for botanists, and DEX for fishers
3. Bait and lures (for fishing only)
ex.) At a certain grade and difficulty, having the appropriate rank, DEX value, and bait/lure will ensure that jigging the rod precisely in the middle will result in a black eel hit.