Hello, we have neem trees planted in Venezuela. They produce viable offspring in northwestern (semiarid) part of the country. Perhaps they are killing birds that eat their fruits.
Besides Indian sub-continent (India, Pakistan, Bangladesh, Sri Lanka, Nepal and Bhutan), neem trees have been reported from Algeria, Angola, Antigua and Barbuda, Argentina, Australia, Barbados, Benin, Botswana, Brazil, Burkina Faso, Burundi, Cameroon, Cape Verde, Central African Republic, Chad, Chile, China, Colombia, Congo, Cote d'Ivoire, Cuba, Democratic Republic of Congo, Djibouti, Dominica, Dominican Republic, Ecuador, Egypt, Equatorial Guinea, Eritrea, Ethiopia, Fiji, French Guiana, Gabon, Gambia, Ghana, Guatemala, Guinea, Guinea-Bissau, Guyana, Haiti, Honduras, Indonesia, Jamaica, Kenya, Lesotho, Liberia, Libyan Arab Jamahiriya, Madagascar, Malaysia, Malawi, Mali, Mauritania, Mauritius, Mexico, Morocco, Mozambique, Myanmar, Namibia, Nepal, Nicaragua, Nigeria, Panama, Paraguay, Peru, Philippines, Puerto Rico, Rwanda, Sao Tome et Principe, Saudi Arabia, Senegal, Seychelles, Sierra Leone, Singapore, Somalia, South Africa, St Lucia, St Vincent and the Grenadines, Sudan, Surinam, Swaziland, Tanzania, Thailand, Togo, Trinidad and Tobago, Tunisia, Uganda, Uruguay, US, Venezuela, Virgin Islands (US), Zambia and Zimbabwe.
Neem trees were grown in a large number of countries besides India including Argentina, China, Brazil, Egypt, Australia, Ethiopia, Sri Lanka, Mexico......etc.