You are not doing a very good job of describing what we are looking at here.
"Manual Shifting"? Is the car a manual or automatic? I suspect auto and I suspect you don't mean "manual shifting" but I have no idea what you MIGHT mean.

"Act like it is downshifting"... so the car lurches and slow and the tach jumps up to higher rpms? That is a downshift, but why would the car downshift unless you are hitting it hard and causing a downshift? (Assuming an automatic.)

It will shift, then suddenly "pull back"... " Again, I don't understand what you are trying to say.