There are two main groups of NM blockers: non-depolarizing (e.g. tubocurarine) and depolarizing (succinylcholine). They both act on nicotinic ACh receptors on skeletal muscle. Non-depolarizing NM blockers are straightforward competitive antagonists for these receptors. As such, administration of an AChE inhibitor (such as neostigmine) would increase the levels of ACh in the NM junction and thus reverse the action of non-depolarizing NM blockers.
Compared to the non-depolarizing agents, depolarizing succinylcholine is an agonist on nicotinic ACh receptors. That's why administration of succinylcholine initially causes depolarization, which is clinically manifested as twitching. However, continuous depolarization results in relaxation and paralysis. During initial depolarization, administration of neostigmine will increase the depolarization (in other words, the patient would twitch more). During the later phase, neostigmine will reverse the action of succinylcholine.
