DMA participate in the reaction is posible that DMA  has a enviromentally effect since it can be toxic to humans despite that it has a boiling point around of 194 °C. During cured process can be ocurr some evaporation of DMA.

I agree with Edwin, dimethylaniline (DMA) participates in the reaction and will become end groups on the polystyrene of the unsaturated polyester resin; assuming styrene is the reactive diluent. There is no -NH2, DMA is a tertiary amine containing -N(CH3)2 groups on benzene. DMA assists the peroxide to form radicals at a lower temperature by reacting with benzoyl peroxide (BPO) to form a benzoyl radical, a DMA radical with radical on N, and benzoate anion. Thermal only radical formation from BPO will give two benzoyl radicals. There will be benzoate (or benzoic acid) and unreacted DMA, as well as much unpolymerised styrene in the resin - each of these is volatile and contribute to the odour of cured unsaturated polyester resin. You may have cobalt present as well since this is a redox accelerator of the initiation. Curing of these resins is generally exposed to oxygen that is a retarder, so more styrene will be unreacted than if it were polymerised to polystyrene in a controlled isolated reactor.

Thanks for information @Robert and Edwin