I seek to ascertain if the moderator should consistently counteract the direction of the main effect of the independent variable, while one intend to better understand how these variables interact and influence each other in statistical analysis.
A variable in a specific model only be characterized as a moderator if it interacts with some other IV(s) as regards resultant scores on some DV.
That is, while the IV(s) may well have some direct impact on the DV (referred to as "main effect/s" in anova-type models)--as might the moderator, there must be some interaction as well. That is, mean effect sizes of the IV(s) and moderator are themselves insufficient for accurate estimation of scores on the DV. For this reason, in the presence of moderation (or interaction), one generally pays more attention to the nature of that moderation/interaction and less attention to the main effect/s.
The influence of the moderator might or might not be that of "counteracting" the influence of the IV(s) in question. Rather, it could be that resultant mean differences on the DV are simply magnified or made smaller by virtue of specific IV/moderator combinations or values (as opposed to so-called disordinal interaction effects).