Madeira is not mentioned in the list of islands in the Atlantic on the species account of Common Waxbill (Payne et al. 2018). The species is considered introduced in Madeira by recent authors (García-del-Rey 2011). Some photographs obtained at the river bed in Machico confirms the species is still present.
References
García-del-Rey, E. (2011). Aves de Macaronesia. Azores, Madeira, Islas Canarias, Cabo Verde. Lynx Edicions, Barcelona.
Payne, R., Bonan, A. & Kirwan, G.M. (2018). Common Waxbill (Estrilda astrild). In: del Hoyo, J., Elliott, A., Sargatal, J., Christie, D.A. & de Juana, E. (eds.). Handbook of the Birds of the World Alive. Lynx Edicions, Barcelona. (retrieved from https://www.hbw.com/node/61115 on 27 March 2018).
Common Waxbill at Machico, Madeira