Recall the electromeric effect

The electromeric effect is the complete transfer of the shared pair of $\pi$-electrons of a multiple bond to one of the bonded atoms, only in the presence of an attacking reagent. It is a temporary effect.

Check each statement

A: The electromeric effect is, temporary effect
This is correct because the electromeric effect exists only during the attack of a reagent and disappears when the reagent is removed.

B: Hydrogen ion $(\mathrm{H}^+)$ shows negative electromeric effect
This is incorrect.
A positive reagent like $\mathrm{H}^+$ attracts the $\pi$-electron pair towards itself. This corresponds to the positive electromeric effect ($+E$ effect), not negative electromeric effect.

C: The organic compound shows electromeric effect in the presence of the reagent only.
This is correct by definition of the electromeric effect.

D: Electromeric effect dominates over inductive effect
This is correct because electromeric effect involves complete transfer of $\pi$-electrons and is stronger than the partial displacement seen in the inductive effect.

Conclusion

The incorrect statement is: $\boxed{\text{B}}$

Comparison with stored answer

Stored correct answer = B
Derived answer = B
Hence, they agree.