Strange Strength Imbalace in Shoulders

I used yesterday one of your shoulder combos - Javelin press++Single iron cross. One side was stronger on the press, the other on the hold! Is that something you encounter, and should be handled like any other?
Now that I think about it, the right side press (the weaker) is also slower at bench press, as is visible when I warmup with one plate (so its fast): always the right side’s plate moves a bit out on the bar.

p.s. the Javelin is great fun! the long bar (20kg std) was all over the place, and I was constantly correcting (standing near a mirror made it more interesting!). It will probably be under control in 2-3 sessions…