The importance of multi-electron dynamics during the tunnel ionization of a correlated quantum system is investigated. By comparison of the solution of the time-dependent Schru007fodinger equation (TDSE) with the time-dependent configuration interaction singles approach (TDCIS), we demonstrate the importance of a multi-electron description of the tunnel ionization process especially for weakly confined quantum systems. Within this context, we observe that adiabatic driving by an intense light field can even enhance the correlations between still trapped electrons.