Effect of ethanol and detergent on cell membranes problem
Detergent and membranes
Moderate concentrations of non-ionic detergents facilitate lysis of cells. This can be exploited for extracting soluble proteins, often in their native form (ThermoFisher). Detergents affect the membrane at concentrations lower even than those that cause an increase in membrane solubility (Ahyayauch et al., 2010). Two ways this manifests is an alteration of the flip-flop effect (the lipid action caused by flipases) and leakage.
Note that the relationship between detergents and membranes aren't mechanistically well understood, and there aren't yet good general mechanistic rules that explain the relationship between concentration and permeability.
Your experiment

The absorbency rate was higher for the 20% and 40% detergent than it was for the 100%. It seemed as though the results were backwards.

It depends on your specific experiment, but typically the higher concentrations will more readily lyse the cell/make them more permeable. It's hard to say exactly what went wrong here without more information. Unless you were using an exotic detergent, it is quite likely that there was an experimental error and the test should be repeated. Alternatively, the results have been misinterpreted and indeed at lower concentrations, there was no cell lysis, and at 100% there are no cells left intact or something along those lines.