You have been misled. An alpha particle decay is exactly that - the unstable nucleus emits an alpha particle, which is a He nucleus (2 protons and 2 neutrons). Radioactive decay is not an "atomic" process.
The emitted alpha particles (He nuclei) have a +2 positive charge. They leave behind a negatively charged daughter atom (a di-anion). The di-anion also won't be around long; it recoils from the alpha particle emission and will interact with its surroundings, passing on the spare electrons. It is partly this process that releases heat in radioactive materials.
The alpha particles do not go very far unless they are in a vacuum. In air, they travel typically a few cm before interacting with other atoms and picking up a couple of electrons to become He atoms.